Yes – the pumpkin bomb is basically like a delayed DoT, nothing happens until the 3rd turn when it all comes at once. Or if the target is killed by an ally that same turn, then the nearby “DoT” activates.
He is kind of like an even more extreme version of Lady Locke in 3* rarity – keeping in mind that 3*s don’t have much HP, that bomb is strong!
It is worth noting though that you can cleanse the bomb before it goes off too, which is easy to do if you have cTyrum available in your 3* bench. Defensively I don’t think Jack is going to be that great, offensively however he’s a pretty strong 3*.