Does the thousand tail watcher give -3 might to my units even if I play my units after the thousand enters in game?

No, Thousand-Tailed Watcher does not affect units played after its ability has already resolved.

According to RiftJudge FAQ (ID 6445, 10209), the Thousand-Tailed Watcher's "When you play me" (WYPM) ability "snapshots" the battlefield at the moment it resolves. It applies the -3 Might reduction only to enemy units currently on the board at that specific time.

Here is the breakdown of how the timing works:

1. Play: You or your opponent plays Thousand-Tailed Watcher. Its ability enters the chain.
2. Snapshot: When the ability resolves, the game checks the battlefield and applies the -3 Might reduction (to a minimum of 1 Might) to all enemy units present at that moment.
3. Completion: The effect finishes resolving and does not persist.
4. Subsequent Units: Any unit that enters play after that ability has already resolved—whether it is played as a new action or flipped face-up from a hidden state—is not affected by the reduction.

Important Note: If you play a unit in response to the Thousand-Tailed Watcher's ability (while it is still on the chain), that unit will be on the board when the ability resolves and will be affected by the -3 Might reduction (RiftJudge FAQ ID 2236).