I have heard reports of wax apple growing in SoCal, but have not heard any reports of them growing in Arizona. Phoenix is going to be a step more difficult than SoCal, with slightly colder winters and hotter summers (hot is not good in this case because it can cause them to dry out).
If you do want to try to see if it can grow in your climate, I would strongly recommend a sheltered location where it will not receive direct afternoon sun in the Summer, with the sun directly overhead. Preferably in a spot surrounded by other shaded plants and sheltered from wind to help hold in just a little bit of humidity. This will also help to reduce the severity of cold temperatures a little bit as well.
Keep in mind Syzygium samarangense ( "Java apple", white color flowers, better eating quality) is believed to be a little bit more cold tolerant than Syzygium malaccense ( "Malay apple", magenta color flowers, also known as "Hawaiian Mountain Apple" ). However, I don't really know if this is true, and in any case I've seen large pots of both growing outside in a nursery in San Diego, in the middle of Winter, but I think that's zone 10b.
Just to clarify, those other reports I have seen were only of samarangense growing in California (one in Anaheim and the other in La Palma), although I did come across someone growing malaccense in zone 10b Florida, although he said it was recovering from the Winter. (not absolutely sure if this implies malaccense is more vulnerable, because zone 10b in Florida can have slightly colder freeze events than 10b in California, which gets glossed over in the averages)
