Autistics and Nurturing Parenting
It is good that you want to build responsibility in your children while being mindful of their developmental stage and being respectful of their autonomy.
If till now you've been using rewards and punishments, withholding and nagging, conditioning and manipulation, etc., first there must necessarily be a WHOLE LOT of undoing that harm. Because the relationship is not one of nurturing but of training, not one of good means and good ends, but what worked' and maybe 'no matter what'.
Some parents will say 'oh, well, it's too late'. It is never too late to apologise, make amends, change ways and achieve whatever good outcome you can in the short remaining time you have as the main people in your child's life for now. Trying IS making amends. A child WILL notice the difference.
Then you can consider a range of intrinsic encouragements from the following:
1. Natural Consequencing
Explain the natural consequences of not cleaning up. For example, if toys are left out, they might get lost or broken. Let them experience these consequences naturally in order to come to understand over time the importance of tidying up. Later on as employees and employers they'll need to deeply comprehend that money is not a reward for doing work, but the handing-over of the just amount of time (consequence, in the form of money) in return for the time given (action, in the form of work).
2. Collaborating
By sharing the task of cleaning-up until they are able to accomplish all of the task by themself, acknowledging their effort, their growth, not just in words or signs, but by matching that growth with more autonomy, self-responsibility, choice that you directly relate back to what growth they've shown you. Maintain the linkage. At family meetings you can discuss when tidying gets done, when it is needed, how quickly it is got out the way.......... and why. You can listen to children's inputs. They may have alternate ideas, even individual ones. Collaboration helps child 'buy-in' to a task, ownership of both the problem ... and the solution.
3. Modelling
By cleaning-up after yourself, and asking other older people to do likewise, noting when you have failed to do so, and the consequences that put on you, that you put upon yourself, and that you cheerily accepted. Children learn by watching, and they watch the good and the bad. Consistency must be household wide. A discussion might be needed about how other households operate. You can say out loud "you get pocket money because you need it and we love you, you help around the house because we need your help and you love us, and these two will not be connected and confused here any more, this is a family based on love, not on 'what tricks work' anymore.
4. Embracing
There is joy to be found in work, especially if attention is paid to how a task is embraced. It is a central nurturing to reveal that to children and watch how that unfolds in a child. Cleaning can be fun, can be made less onerous, can be made fun, a game even. It can become 'beat the clock' with a timer, or be accompanied by quality parent-child communication, or a song and dance routine, and a reluctant child can write down on a piece of paper that being asked to tidy is like a life-wrecking proposition and afterwards acknowledge on the same piece of paper that it wasn't at all, there was satisfaction, it had a start and finish that were not far apart, that some aspects were more preferable to others, whatever. These can be kept as a reminder, leading to trust when asked to have a break in their day to assist.
5. Choosing
Giving a child choices tends to empower them, grant a measure of appropriate control, and show respect for their voice, the essence of their being. You can ask them "Would you like to put away the trucks while I scoop up the torn paper?" or "How about you pick things up and hand them to me at the door to go put in the right place? Or would you like to do that?" This helps them feel more involved and invested in decisioning.
6. Sizing
State the task clearly so their can be no misunderstanding, no 'how long is a piece of string' anxiety in your child. Instead of saying, "Clean up the room," you might say "make these toys in this area go away to a good place" and then focus on improving how good a place they go to on another succession of days. You might break it down into smaller more <mentally> and physically manageable tasks, like "First, you could put the blocks back in the block box", and later "hang your rain coat up on the hook and come back for one more job". Start small and build. That's vital if the intrinsic motivational connection is weak because rewards have been traditionally accepted. You are looking for progression from scratch that is ongoing, not some burst of activity on day one.
7. Patterning
Starting from scratch you can develop a habit, a routine, an expectation based around the idea 'if this pattern of getting things done works well for us, we should keep it going in order to simplify life and create really good spaces for play and what else we want to do'. That could look like always cleaning-up before dinner, not waiting till a child is more likely to be tired later on, or to feel like they've not finished playing if done earlier. While children can thrive on rituals and routines, they need to be based in justice, able to be amended, and have built-on alternatives if a child just cannot follow them or finds themself wanting to break-out into diversity or experiment occasionally with a new way of doing things.
8. Empathising
To empathise is not to excuse, it examines reasoning and considers weightily the perspective of your child. When you acknowledge a child wants to keep playing as clean-up time approaches before dinner, and say 'I was always like that to when I was your age', you wrap understanding around your child and make it more possible for them to respond willingly. Waiting to play again might seem to them like forever, but here is where parents can get creative about explaining just how short a time that really is, or chime in with what lies in store as possibilities. Dinner, after all, makes play possible.
9. Transitioning
Many autistics especially have an issue with transitioning and micro-transitioning because of monotropism, in the same way that many children in wheelchairs aren't great at getting cans of spaghetti down from the top shelf. Disability remains disability. What is an age-appropriate expectation for one child, may not be plainly for yours. Is there a task your child can opt-out of in return for doing more of something they are proficient at or keen about? Peeling potatoes over picking-up toys?
How transitioning might look is when your child says they don't care about the mess, it's fine with them, and they want to keep playing, you might respond with something like:
"I hear that you want to keep playing, and I understand it's fun. But we need to put the toys away so they don't get lost or broken. How about we set a timer for 5 minutes, and whatever we can clean up in that time, we'll do together. Then you can get back to your game. Or how about I set the timer for 10 minutes more play and we clean-up when it rings?" I fully no how much easy it is to say 'Do this now or else', just as I fully know a child can fall silent or respond with 'do it yourself'. But we choose the good-hard road to growth, not the bad easy path to tidy, everytime.
10. Conclusion
"But it's how my parents brought me up and look how I turned out.
At some point the whole concept of children-as-property, basically animals to be trained to another's normalisation, needs to be clutched, as though a grenade, by all parents, and fallen upon. There are other ways that have proven to be sound, workable over time, that keep children in that children-as-a-gift zone thoroughly, that keep children so far away from 'the end (obedience, normalisation, conformity) is justified by the means (manipulation, nagging, anxiety-ramping, hurt)'. How far? Infinity far. The Devil must not get his way.