The 6 yr old brain is only just starting to understand consequences - and if you're going to use consequences, it needs to be directly connected to what happened and not delayed.
As PP have said, losing an ice cream the next day will make him sad but his brain isn't yet mature enough for that to influence his decision-making or his behaviour.
Consequences are quite a sophisticated concept and although your child may appear to superficially understand, at 6 years old they're not developmentally able to properly grasp the concept or link the two things in a useful and effective way. He may seem to know why he's not getting ice cream but it won't have any impact on future behaviour because his brain isn't developed enough yet to be able to do that.
That's not "letting him get away with it" or not having boundaries, it's about age-appropriate consequences rather than punitive consequences which don't actually have any effect.
One website had a good explanation of consequences for 6-10 yr olds:
"Use logical consequences: Otherwise known as cause and effect, these should be directly related to your child’s behaviour. If your eight-year-old is late for school because she had trouble getting up in the morning, make bedtime earlier the next few nights rather than revoking her TV privileges."
However, while I don't agree about taking away his ice cream, I think if you say you're going to do something you should follow through. So if you've said you're going to take away his ice cream, then I don't think you should backtrack. I think offering him the chance to "earn" his ice cream back is a good way to remedy the situation. I don't normally agree with food being used as a treat or a sanction, but on this occasion I think it's probably the way to go because of the consequence you used.
I've got two autistic DC and big emotions are hard for them to handle. And emotions are much more likely to come spilling out when they're tired and not as able to regulate themselves properly, which sounds like what happened here. For me, it's natural consequences every time, rather than a "punishment" that isn't linked to what they did.