Mordecai's original exit deal was for a certain number of cycles, but it would only count this one as complete if Carl and Donut made it to the 4th floor.
If they'd died, he'd still be indentured in the dungeon next season.
The manager perk actually has nothing to do with it, other than having the unfortunate side effect of making him stay involved in this season/cycle for longer before he can pack his bags and GTFO.