The TZ for the machine is based upon the address of the location the game is registered. When a game is connected to Stern Insider Connect the time of day is automatically maintained, and corrected for TZ and DST. The machine uses local time. Provided they play on May the 4th and log into Insider Connected, the player will receive the achievement.
I think the confusion is around the Insider portal, which seems to track stats on UTC time only. Since the achievements aren’t shown with a time stamp, do we know for sure whether they’re added with the game’s local time or the “connected” time, which is UTC. If the latter, the May the 4th achievements could potentially fall on the wrong day no?
Provided they play on May the 4th (midnight to 11:59pm in the local time of the game location) and log into Insider Connected, the player will receive the achievement.
From my analysis on that game at Riverside Game Lab, no achievements were being given out yet scores were recorded on the Insider site…maybe achievements have to be enabled in a setting?