Surely you are using a push stick, right?
It sounds to me like bandsaws are the most dangerous tool in your shop, you need to remove that nonchalance from your mind, next time you might not be so lucky.

Every tool room I ever walked in had guys with fingers missing, it can't be fun looking for a finger tip on the floor and then putting it in a matchbox hoping they can sew it back on at the hospital. However, if you do end up in that situation make sure that you put it on ice, the tissue remains viable for longer.