It appears that waiting is up to however is administering the shot - even in the same location. My husband and I both got our boosters at the same location. He was told to wait 15 minutes, I was handed back my shot card and told I was good to go. He got Moderna, I got Pfizer.Eh, people receiving the same brand booster don't have to hang around the 15 minutes afterwards. There is limited waiting areas where available. i.e. go stand in this corner for 15 minutes. The local hospital is vaccinating 5-11yos only.
So it may be dependent on brand, location, or whoever is administering the shot - especially if they had someone with a bad reaction in the past! But there is no reason to argue about it.