We purchased all-inclusive tickets, so we used their equipment. We used one deposit for both of us (this was just for the snorkel mask, fins, life jacket, snorkel tube). We left our hotel room key and had no problems. With our coupons we got a locker and towel, and those didn't require a deposit.
I would assume (again I'm not sure) that you don't need to leave a deposit for the innertubes (I'm assuming you mean the "lazy river" portion). We didn't need to leave anything when we went to get an innertube for both of us. However, we carried all our belongings with us (towel and snorkel equipment). I did notice that for people that wanted to put their stuff in the bag, you might have to leave a deposit. They bring this locked bag down the river for you. At first we wanted to leave our snorkel equipment, but they wouldn't let us put it in the their bags! It seemed like the bags were only for people that first got into the park and decided to do the lazy river first before getting a locker, thus they needed to leave everything they brought with them (ie backpacks, shoes, clothes).
Actually, it was a good thing that we had to carry our snorkel equipment with us. The lazy river is almost "too lazy". Luckily we had our fins and we used these to paddle down the river!