If Thousand Tailed Watcher is played and later in the turn the opponent plays a reaction speed unit (like Shen or Teemo) from hidden, will those units have the -3 applied to them?

Ruling: No, units played after Thousand Tailed Watcher resolves will not have the -3 applied to them. Thousand Tail and other spells and abilities that change stats do so when they resolve, and the amount added/removed and the number of units affected aren't updated until the effect wears off.

Nuances:

• The exception is for passive abilities (like a battlefield that constantly gives everything +1), which continuously update. Thousand Tail is a triggered ability (indicated by 'When' in 'When you play me'), not a passive ability.