If my opponent moves both Hwei and Vex Apathetic to a battlefield together, can I react to the Hwei movement and flip my hidden Purple Teemo at a battlefield, so that he is not stunned because he is played before Vex is "at" the battlefield?

The Ruling

No, you cannot prevent Teemo from being stunned in this scenario. Even if you reveal and play Teemo as a reaction to your opponent moving Hwei and Vex to your battlefield, Vex’s ability will still stun him.

Reasoning

1. Vex's Trigger Condition: Vex, Apathetic has the triggered ability: "When an opponent plays a unit while I'm at a battlefield, [Stun] it." This ability triggers based on the unit being played while Vex is present on the board.
2. State-Based Triggering: Even if your opponent moves Hwei and Vex as a single game action, Vex is considered to be at the battlefield from the moment the battlefield is reached. Because the act of revealing and playing a hidden unit occurs while that battlefield is occupied by Vex, the condition for her trigger is met.
3. No "Before" Window: You cannot play Teemo "before" Vex arrives because the move is a single, simultaneous event. Once the move is processed, Vex is present at the battlefield. Any reaction you take—such as revealing and playing Teemo—occurs while Vex is already at that location.
4. Chain Resolution:
   • You reveal and play Teemo from hidden as a reaction.
   • Teemo enters the battlefield.
   • Vex's ability triggers: "When an opponent plays a unit [Teemo] while I'm at a battlefield."
   • Vex's ability is added to the chain.
   • When the chain resolves (LIFO), Vex's ability resolves and stuns Teemo.

Important Considerations

• Sequential vs. Simultaneous: While moves may occur "together," the game state updates to reflect the new location of all involved units simultaneously. Vex does not have a "travel time" during which she is not yet considered to be at the destination.
• Rule 383.2.c: Triggered abilities evaluate their conditions once the inciting event has been processed. Because Teemo is played after the units have moved, Vex is already established at the battlefield, fulfilling the condition "while I'm at a battlefield."

This interpretation is based on the standard chain rules (Rule 383.3) and the triggering mechanic of Vex, Apathetic as clarified in RiftJudge FAQ #9240, which confirms that Vex stuns any enemy unit played while she is present at a battlefield.

Note: I could not fully verify this ruling against the retrieved rules.