I have the same computer and it turns on automatically provided the battery is still good. I usually turn it on myself to check that the gas is set correctly when gearing up to match what I have in the rental or my own tanks.Thanks a lot! I didn't know that. I've seen that my computer (a Cressi Leonardo), according to the instruction manual, gets automatically into the dive program "DIVE AIR" when you reach a depth of 1.2 meters. But I don't know whether that means it'll turn itself on if it's turned off, or it needs to be already on and will get into the dive program if you are in the "DIVE SET" program instead.
I'll check in my next dive. I'll jump into the water with it off, will go down to 1.2 meters and see what happens. If it doesn't turn on automatically, I'll surface, turn it on and start the dive again.