The idea that Iran has some sort of magical sway over Shia everywhere is a common exaggeration and bit of foolishness that is promoted by the media but is just not correct.

Furthermore you can't underestimate the power of nationalism which trumps religious affinity. Baathism was strongly nationalistic as well as secular so people who were nominally Shia could be members of the regime if they were secular and nationalistic and in fact there were high ranking officials in his regime who were nominally Shia. And of course anyone who refused to fight would be shot.