Does the Thousand Tailed Watcher apply its debuff to units played after it?

No, Thousand-Tailed Watcher does not apply its debuff to units played after it.

According to the RiftJudge FAQ (ID 6445, 8344, and 2350), the Thousand-Tailed Watcher's ability "snapshots" the battlefield when it resolves. It applies the -3 Might reduction only to enemy units currently in play at the moment the ability resolves.

Here is how the timing works:

1. Play: You play Thousand-Tailed Watcher. Its "When you play me" ability enters the chain.
2. Snapshot: When that ability resolves, the game checks the battlefield and applies a -3 Might reduction (to a minimum of 1 Might) to all enemy units currently present.
3. Completion: The effect is then complete. It does not linger or create an ongoing aura.
4. Subsequent Units: If any unit enters play after the Watcher's ability has already resolved (such as a unit played as a later action, or a unit flipped face-up from a hidden state after the resolution), that unit is not affected by the -3 Might reduction.

Note: If a unit is played as a reaction to the Watcher's "When you play me" trigger (or to a reaction on the same chain), that unit would be on the board when the trigger resolves and would be affected.