In general, abilities only power up moves of the user.
Hence, Technician of your own Pokemon does not boost the power of the opponent's moves.
The exception to these are field effects brought about by abilities, like Weather or Terrain.
Here is a replay from PS! if you want that as source.
This is what Technician Scizor's Bullet Punch reads as :
whereas Swarm Scizor's Bullet Punch has this description: