Tuvok had been captured and programmed to be a sleeper agent who reacted to a trigger years earlier when he was still in the AQ.
All the hard stuff had been done, the activation could have been as simple as saying the word "teapot" but you're right they made it look like Bajoran magic for some reason.
Anyone Tuvok had had a serious meld with over the years should have "caught" his sleeper programming (and siphilus).
Neelix and Janeway come to mind.
If the Devore had been allowed to take Tuvok to a concentration camp, none of those murders would have taken place.