Does Tribal Forcemage benefit from its own morph ability?

Yes, it does.

The ability is a triggered ability, which means it must go on the stack and then resolve before anything happens. By the time it does something, Tribal Forcemage has already been turned face up and is just like any other normal Elf Wizard creature.

In this particular case, Tribal Forcemage is already a normal Elf Wizard even by the time the ability triggers, because it only triggers after it has been turned face up. But even if it weren't, the triggered ability still must be placed on the stack the next time a player would receive priority, and then resolve when players pass priority, all before it matters. Theoretically during that time, before it resolves, Tribal Forcemage could change types, or be Cloudshifted away and back, etc. But it would still count as long as it is on the battlefield and is the matching type when the triggered ability resolves.

If Tribal Forcemage or any other Elf (assuming you chose Elf) entered the battlefield after the triggered ability resolved, it would not get the benefit from it:

611.2c If a continuous effect generated by the resolution of a spell or ability modifies the characteristics or changes the controller of any objects, the set of objects it affects is determined when that continuous effect begins. After that point, the set won’t change.