NAP should probably have been more accurate with their statement, if they didn't want AP to regain priority in their main phase.
"During your end phase, I cast
Jin-Gitaxias, Core Augur“ would clearly occur after the main phase, and before the Cleanup step in End Phase. That might have the desired result, of wiping out AP's hand in their Cleanup step… or AP might have an Instant to deal with J-G, Hand Eater.
However, what was said was clear, even if not what NAP really wanted: ”At the end of your main phase". That means that, once J-G, Major Annoyance resolves, AP will again have priority during his or her main phase.
Thanks! - Scott Marshall, L5, Denver; Judge Forums NetRep