I think that you are being confused by the termonology. If you live in a typical residential area, you have single phase 240 volt service. The transformer on the local pole is center tapped, so that your home is supplied with two 120 volt legs. Only heavy industrial areas have true three phase service. The 3X16 service that you refer to is most probably 3ea. 16 amp loads ,probably on 3ea 20 amp breakers. (Could be either single leg 120 volts or dual leg 240 volts.) If they are 120 volt breakers and you have 3 ea. 16 amp loads on two legs, there is going to be unequal loading, wether you have 2 loads on leg A and 1 load on leg B, or 1 load on leg A and 2 loads on leg B. If they are all 240 breakers, then the loading of both legs is equal. Hope that my explanation helps and doesn't further confuse you.
EDIT: Tubs come with either 120 volt or 240 volt pumps and heaters, so without seeing the breakers, equiptment or a schematic of your tub, it is impossible to tell what you have going on.