The form is locked in when you originally catch the Scatterbug. In the game's data there are 20 forms of Scatterbug, one for for each of the patterns. Same for Spewpa. (You can see in datamines they are labelled from Scatterbug, Scatterbug-1 and so on up to Scatterbug-19.)
I just tested this to verify - I sent a Tundra postcard to Violet earlier and the Vivillon that appear are Tundra. But an old Scatterbug I caught a while back still evolved into the Fancy Pattern. A new Scatterbug, caught after sending the postcard, evolved into the Tundra Pattern. That Scatterbug would stay Tundra forever even after sending a different postcard.