I recently had a taxi driver from Iran who was able to leave as a religious refugee. Anyway I asked about who is really in charge in Iran. He said it’s the Ayatollahs and not the president. He is just their puppet/mouthpiece. So “reining in the president” can’t happen other than as a charade.
I believe the point of the article is that there are factions within the Iranian leadership that are encouraging (pressuring?) Khamenei to yank the president’s chain.