Does Vex Apathetic stun reflection tokens when they are played?

Yes, Vex, Apathetic will stun Reflection tokens when they are played, provided that Vex is located at a battlefield at that time.

According to RiftJudge FAQs #8758, #9485, and #9859, the interaction works as follows:

1. Trigger Condition: Vex, Apathetic has the triggered ability: "When an opponent plays a unit while I'm at a battlefield, [Stun] it. They can't move it this turn."
2. Playing a Token: In Riftbound, a token is considered "played" if the card effect that generates it explicitly uses the word "play" in its text (e.g., "play a ready Reflection unit token"). Because these effects satisfy the "plays a unit" condition, they trigger Vex's ability.
3. Programmatic Selection: As clarified in RiftJudge FAQ #9625, Vex's ability uses programmatic selection rather than targeting. This means it will successfully stun these tokens even if they possess protections against being chosen by enemy spells or abilities.
4. Result: When the Reflection token is played, Vex's ability is placed on the chain. Upon resolution, the token is Stunned and gains the restriction that it cannot move for the remainder of the turn.

As noted in RiftJudge FAQ #8746, the stun lasts until the beginning of the next Ending Step (which, in a 1v1 match, will be the active player's Ending Step), but the movement restriction remains in effect for the entire turn.