is there a top to your bettas tank? is there a filter? if not than I would say dont burn them in that room because there is parfum in incense and it will settle in the water and could harm them.
I dont think burning insence in a room would cause any harm if their tops are covered and your keeping the water clean. If you were laying your jostick over the tank allowing it to drip into the water well yes there would be a problem...lol Are you continuisly burning a jostick in your room and not allowing the air to clear??? I burn insence too.
I've always burned incense in the same room as my fish, they don't seem to be effected. So long as there is a cover for the tank and you aren't constantly burning it, it should be fine. Try to place the stick or cone or whatever on the other side of the room just so the concentration is lowest near the tank if you want to be on the safe side.
