Even though on Paint Smudger’s description it says “whenever you CAST a spell”, and Temporal Tampering’s description is “your tavern spells CAST TWICE”, smudger casts the blood gem only once
Spells cast by an external source do not count as cast by you.
As a player you cast your spells once. The second cast is performed by another effect, you didn’t cast it.
Good way to tell if you are casting it twice is if you are spending the resources to cast it twice. If not, then you aren’t gonna get those types of reactions you originally thought you would.