If my opponent put a Stage 1 Pokemon directly into play using Tatsugiri ex's "Cinnabar Lure" attack, and I use Paldean Tauros' "Spirited Tackle" attack while that Pokemon is Active, would it do 90 or 180 damage?

It does 180 damage. Although the Stage 1 Pokemon is not an "Evolved Pokemon" in this scenario, it is still considered an "Evolution Pokemon" (Stage 1) that meets the requirements for Spirited Tackle.

Relevant cards

SV8_142

SV8_18