If you play Thousand-Tailed Watcher with Ahri, Confident in base, if I attack with Ahri, does she see the might reduction caused by the Watcher and get a +1 might for each unit that was at that battlefield? Or does she need to be at the battlefield in order to get the additional might?

No — Ahri, Confident has to be at that battlefield when the Might actually comes down. Sitting in Base when Thousand-Tailed Watcher resolves, she sees nothing, and moving her in later doesn't retroactively create the trigger.

"Here" in her second ability is part of the trigger condition, so it's checked at the moment the reduction happens (Rule 359.3.f.3), not when you later attack. Watcher's "when you play me" is a single board-wide –3 on enemy units — those units get reduced at their own locations, and none of them are at your Base. So Ahri gains nothing from it, and there's no per-unit bonus to collect for units that were at a battlefield she wasn't at.

What does work: when Ahri attacks, her own Disarm gives an enemy unit here –1, and that's a real reduction at her location — so she gets +1 Might from it, as long as the defender is Might 2 or higher (a 1-Might unit snapshots to –0, so nothing was reduced; Rule 479.4.b).