If a user gets question banned after asking a new question but that question then gets migrated to another site, is the question still taken into account when calculating whether the user has a question ban?

I remember that I asked a question on an SE site and I immediately reached the limit - it didn't matter if it was upvoted/answered. In my memory, the first reactions were positive including a couple of upvotes, maybe even an answer. The question then got migrated and the "ban" was immediately lifted (as opposed to having to wait for a couple of months for it).

The Question ban FAQ states:

Additionally, for question bans, the fact that a question is deleted counts against you, if others have invested time into answering or moderating the question.

Migrated questions are deleted - does this count against the user? My memory of being unbanned seems to indicate it does not but it's not clear.

Edit trying to make my point clear

I am happy that someone tried to improve the question but the question was not limited to a question ban it included badges too. And it certainly wasn't restricted to a post-ban situation. Another similar situation is when the question is migrated before the question ban (if any happens). Let's say the person has N questions before the "ban" if some N-Xth question get's migrated before even the Nth question is asked does the N-Xth question still count against?

The migrated question normally counts as a closed question and there is a new question on the recepient.

I had originally asked a different question that was considered a duplicate (I did so especially because this question already has an accepted answer). But it seems that the question community considers it covers the issue below

I understand that the migrated question normally counts as a closed question and there is a new question on the recepient. When the migration is rejected is there a stub left on the previous destination that counts as a closed question? Are there 2 question (a deleted stub and a version migrated back) in the site that the question was originally asked (the original origin)?

How exactly can a wrongful (it wasn't off topic in the origin site and the author didn't ask for it) migration be "corrected" (not just having the question in the Origin site but also not counting as a closed question in the destination site)?