Alot is to do with the concept of time and understanding the passage of time, time management etc.
How they actually 'feel' when there is a change, or there isn't enough time to do everything is hard to gauge apart from their reaction to it.
An expert described it to me as like taking a shower without a shower curtain. For NTs, although we may 'feel' very strongly about things and get very upset when things go wrong, we have more 'control' (ie. the shower curtain) to contain the emotions (ie. the water).
And this 'control' is not just 'learnt', although that is part of it. It is also part of our biological make up that we can 'restrain' ourselves more easily. I think there is evidence of differences in the frontal lobes of those on the spectrum which can mean it is more difficult to control emotions.
I am not saying that those on the spectrum cannot restrain or control themselves. But the extra protection of the 'curtain' may not be there or may only partially be there. It all depends on the functioning level of the person involved.
It is the overwhelming full on flooding of emotions that those on the spectrum can find very hard to cope with and which my son finds very hard to deal with because he himself feels out of control and does not like it and does not like how it makes him say bad words or causes him to be impulsive and behave badly.
There could also be immature development and delays involved as well and therefore you are dealing with the emotional response of a much younger child to the one you have standing in front of you.
How do we cope with it?
Well we have lots of regular talks about what to do when things do go wrong. And we talk and act it through (role play) before there is an actual instance. Sometimes this does help him be more appropriate when something does actually happen. Sometimes it doesn't.
Lots of picture examples of what to do with change ie. story cards that tell a story, but at each stage there are options and choices that will mean a different outcome. Eg. johnny is watching TV and mum says it is time to go to catch the bus. Johnny either (a) turns off the TV and leaves with mum and catches the bus, or (

he refuses to leave until the programme finishes and so they miss the bus and have to wait another 15 mins for the next bus. etc.
I find that very often when the whole process is explained to our children they do get why that particular outcome happened ie. having to wait for the next bus caused johnny and his mum to miss part of the film at the cinema and that made johnny angry and sad. But what our children often cannot do is 'predict' what their current behaviour or choices will have on future options.
Don't know if that is any use at all, as you may well have worked all that out yourself anyway.