Based on this comment from Vic in another blog post, the intent seems to be that everyone who played a spell will do recovery at the end of the turn.
"Because most recharge checks used to happen in the middle of an encounter, everything usually had to stop and wait while those checks were resolved; now, the next player can usually get on with their turn while other players process recovery. (Ok, this isn’t true when the next player also has to do recovery, but since it’s true more often than not, it does save time.)"
The implication here is that the recovery phase speeds the game along, unless the player whose next turn it is has to do recovery before he can start his turn. Thus, off-turn recovery for all spellcasters seems to be the desired intent.