I'm going out on a limb here to say that in MKX triborg is not cannon, but may be in future games.
His story will probably be the same as ermac's in the new timeline, in that there are multiple personalities, with one dominant one. Cyrax will attempt to convince the others to help sub-zero and the other earthrealmers, just like in the comics.
Sektor will attempt to take control of the body forever, so he can rebuild his cyborg army.
Triborg will be the dominant personality, having a lot of stress from constantly having 'shoulder devil/Angels' with him, and will probably be a chaotic neutral guy.
As for triborg himself, he probably got cyber smoke's augments after smoke evaded capture. I think I remember hearing that cyber smoke would have got cyber sub-zero's body, I think triborg was specifically designed for having multiple 'units', one for the two 'generals' (I say that as they are the only ones with a proper colour scheme aside from CSZ) and one for smoke, who was just too cool to waste.
That or it's hydro. Which admittedly would be kind of cool, but I doubt it.