4x4 is a great amount of space to work with. But I would suggest a couple changes to your plan.

If I'm reading this right you probably have much more depth then you need. SFG generally says to start with 6 inches of dirt unless you are putting in something like carrots. My beds are made of 8 inch pine boards with dirt going up just over 6 inches.

As long as you can support the tomato it should be fine in a raised bed. I would actually be more concerned with the melon--melons like to spread and travel. It could take over the whole patio unless you can direct it out of the way.

Last, treated wood can be a contentious topic--some kinds of treated wood is made with chemicals that the EPA says should not be in contact with food crops. I would suggest saving your money and using untreated wood. Especially since this will be raised and on a patio you may be surprised with how well the wood holds up. Good luck and have fun! :)

"If I'm reading this right you probably have much more depth then you need. SFG generally says to start with 6 inches of dirt unless you are putting in something like carrots. My beds are made of 8 inch pine boards with dirt going up just over 6 inches."

6 inches is okay if its going to go out the bottom of the bed, into the ground. He's doing this on a brick patio, so it's essentially a large container (if I'm understanding correctly), and that's going to be a really shallow container for large vegetables.