Raid is triggered by killing non-captain pillagers, even villagers.

At a pillager outpost killed the captain, drinking milk immediately did not cancel bad omen or the raid. No other pillagers had been killed prior. After defeating raid and getting the "Victory" message a pillager (non-captain) spawned and was killed, which triggered another raid which could not be stopped by drinking milk again. Raid was completed and got the "victory" message again. Killed a villager from the village where the outpost was and that started another raid, again drinking milk had no effect.