They have to be on the 25-man roster for the entire season. They have to be active (not on DL), for a minimum of 90 days before their rights are fully acquired. Araujo was on the roster all year last year, but on the DL for all but 73 days, so he had 17 days left to go before we get his rights and can send him down without having to offer him back to the Cubs.
So wait. Basically you have to play a man down if you have a rule 5 guy on your team that is on the DL? How did I not know this?