This is a question that only a structural person can tell you. Its allot of weight on a deck when you consider the tub, water, people in it, movement and what ever other deck items you will have on it. I think you are on the right track. How ever I would personnally change a few items. My deck is about 24" off the ground. I used cement pillars with rebar in them and then the set a bolt in the center of each on and used the deck hangers to put my beams in. Then put my joists on top on 12" on center. The things I would change is I wouldn't cement the 4x4 in the ground, I would pour footings/pillars and use the galvanized brackets to hold your beams in place. For decks its nice to avoid any wood contact with the ground surface. I would also beef up the beams to 2x10 or 2x12 doubled up. Its just a peice of mind knowing your deck is going to last.
Good luck
