If I target Vex Apathetic with the spell Falling Star, do I need to pay the deflect cost for both instances of damage?

Yes, you must pay the Deflect cost twice.

Falling Star has two separate instances of "Deal 3 to a unit," and each instance chooses (targets) a unit. Vex, Apathetic has Deflect (Deflect 1), and per Rule 809.1.c, Deflect imposes an additional cost "for each time they choose me." If you target Vex with both instances, that's two times chosen, so you pay 1 Power twice — totaling 2 Power in Deflect costs on top of Falling Star's base cost of 2 Energy and 2 Power.