As in the title, it seems that going into overwatch with a pistol results in the soldier automatically switching to and firing their main weapon as soon as an enemy shows themselves (thus far only had my heavy and sharpshooter do that, have yet to test whether that also happens with assault rifle/PDW users) despite paying just the pistol’s 25% AP cost.
I noticed that too, but shhhhh they’ll turn off our trick 
From what I saw with my sniper, overwatch uses the main weapon of the soldier, the one they start have in hand during the rooster edit and when the battle begins. I tried to see if there was any difference between the sniper rifles I got, and the sniper ended up having the pistol as a weaponp during overwatch ( and I probably lost a few return fires from my assults when I switched their weapons with the shotgun).
If you want to get the right weapon as main one, just remove all the other ones from the operative’s inventory and then put them back.