Welcome to the site - I'm not exactly in Phoenix. I am a little north of you and I have to take precautions to protect bonsai in this harsher environment than most. If your bonsai came from a grower in San Diego, chances are that the soil is appropriate for here and you won't have to change it for a little while. San Diego is actually a coastal desert with similar (or less) rainfall amounts.
I haven't tried to grow a camelia but the last link Gnome has provided has some good general info. It seems very similar to an Azalea, IMO.
If they are saying partial shade, then give it total shade in Phoenix for the summer - perhaps under a porch - but keep it away from the outside walls of a house that may get hot in the coming months - don't let its' pot (and roots) get too hot.. good article about this:
I wouldn't worry about a repotting now - If it has flowers currently, don't be worried if they dry out very soon.
I find this chart (from Phoenix Bonsai) very helpful:
Pay particular attention to the last on the list... "Summer protection" - I think we have a full gray box now!
"When is it time to water my outdoor bonsai here in Phoenix?"
"It's always time to water your outdoor bonsai here in Phoenix!"
Don't let it dry out - give it a lot of shade or filtered light - half (or less) strength fertilizer once a week - pinch off those flowers when done - regular misting, don't let it freeze (possible - but not probable!)
If you have water from an RO system in your house - use this - it tends to be more on the acidic side - your camelia will live this... if not, add a dinky dash of white vinegar to the water once a month...
Also check out "Baker Nursery" in Phoenix - they have bonsai and help answer some questions too...
When you're ready to repot, I'll give you the secret desert soil recipe!
just kidding - I've been using 2 parts mulch, 1 part turface, 1 part lava rock, 1 part pine bark, - all sifted to remove fine (and large)particles, a handful of sand and when all potted, I layer pine bark or mulch on top... I also use thicker (deeper) pots. Some here sing the praises of Peat Moss in the mix (with regular potting soil), but I have taken a leap of faith by avoiding using it at all - the moment of truth will be a few months or so when most of the hot weather is over... I have to say I have yet to go a summer with this mix, but so far no trees have perished...
and I'm not watering more than normal...
Good luck with your new bonsai - check on it everyday - you'll see what needs to happen to care for it... Hope this helps and I'm sure there's something I've missed... keep reading the Phoenix Bonsai info.
If you're going to keep this thing indoors, well, forget everything I've said!