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(I think Silv summed it up fairly nicely. Tyki is G's pent up darkness turned second personality. Tyki is spawned from DGM, too.)
Joel: Carbuncle! I need your help! G is terribly wounded! I'm doing my best, but he's hurt bad!
G: I'm ok.... *takes deep breath* JOEL! WHY DIDN"T YOU TELL ME ABOUT TYKI?!?!?! I thought I had done all of those things! Do you know how... how... terrible I felt? And that you still hated me so...
Joel: Gav, you should know a few things first. Yes, I knew. Link knew, too. The clan knew, too. That's why I came after you. I was supposed to bring you back. I was told to behave as if you had done it though, because the clan felt that it was our responsibility to help you. I was told to, by whatever means, make you truly believe you had done what you thought you had. When I saw you had new companions, I'll admit I got angry. After all of this time, for me to show up at YOUR call to discover that.... Anyway, when we talked before, and we came to an 'understanding', it wasn't because you got through to me. It was because I believed that your friends would be what you would need to deal with Tyki. I was gonna leave, but I had to keep up appearances. But when you went berserk just because you felt betrayed by Song, for such an insignificant thing, I knew I had to tell you. I'm sorry.
G: *begins weeping* Joel... I'm the one who should be sorry. You should never have done that to that degree. I caused YOU pain. I... I'm sorry.... I did beat Tyki, though. We fought and fought, and destroyed Ganon's castle in the process. I have Innocence now, though. I... I can fight him should he ever return. I may never see again, but that shouldn't matter. I WILL protect everyone I care about from him. From ME.