perhaps they could change it such that experience only updates at the end of the week along with everything else?
So if a player's experience reaches the desired level during mid-week, he doesn't pop until the training update, along with the other skills and GS.
Otherwise, implement the arrow with a timer of 1 week from when it pops. Same as other arrows. If you only look at your playersr once a week to see any training updates, then you will see the experience update then.