Does Thousand-Tail Watcher have to pay Deflect cost?

No, Thousand-Tailed Watcher does not have to pay Deflect costs.

According to official rulings and the mechanics of the Deflect keyword:

1. Deflect only applies to targeting: Rule 735.1.c defines Deflect as a cost imposed on spells and abilities that "choose" (target) the permanent.
2. Thousand-Tailed Watcher does not target: Its ability ("give enemy units -3 might this turn") is a blanket effect that applies to all enemy units. Because you do not select or "choose" specific units for the effect, it does not trigger the additional Power cost from Deflect.

As stated in the official FAQ:

"Thousand-Tailed Watcher does not choose targets when its trigger activates, so you do not need to pay Deflect costs even if your opponent has a Deflect unit."