All the admin probably takes an hour at most; it's an automated process with some identity verification, and most registrars loooove to have you as a customer so they want to make it as easy as possible for you.
There may be a mandatory waiting period.
And finally, there's DNS caches; if you know a migration is upcoming, it's worthwhile setting the TTL to a lower amount.
If you're doing it right, your registrar doesn't run your DNS, so there's no DNS migration. Of course, if your registrar is also doing DNS, email, and web hosting for you, it's messy.
For this poster, I don't think they can migrate to a different registrar while their domain is in the 'redemption' period, and they may not be able to migrate within some time period (30 days?) of renewal, either.
There may be a mandatory waiting period.
And finally, there's DNS caches; if you know a migration is upcoming, it's worthwhile setting the TTL to a lower amount.