We all know that Cloud was helping Hades in the first game out of a deal to help him locate Sephiroth after he would defeat Hercules, and in the next game, Tifa looks for Cloud. She doesn't get much interaction time with Sora, and I personally think that in comparison to the other Final Fantasy VII characters, she's the least promoted. But anyway, back to the main point.

Perhaps the reason why Cloud left Hades was because Tifa intervened. She may have told Hercules that she was looking for Cloud because she believed that he might be participating in a tournament there, and Hercules may have told her that Cloud was working for Hades. Later, after Hades orders Cloud to defeat Sora, due to his progress in the tournaments, Cloud refuses, and Hades sets Cerberus on them, after which Hercules saves them. After this, Cloud would confront Hades about what he did to him and Sora, and then Tifa would arrive and tell Cloud about Hades' true intentions: to use him to kill Hercules. Cloud and Tifa would then battle Hades and end up captured, but Hercules would find them and set them free. Cloud would then apologize for helping Hades, and decides to find Sephiroth on his own. After their battle in the first Final Mix, they disappear, leaving Tifa alone; she then has to start her journey all over again.

In the second game, Tifa encounters Sora and asks him for help in looking for Cloud, though she only describes his characteristics vaguely and does not specifically state his name. She later briefly sees Cloud during the 1,000 heartless battle, but he chases after Sephiroth, leaving her to battle a group of heartless on her own. Much later, after Sephiroth challenges Sora, he tells Cloud about it, and they withness Cloud and Sephiroth battle. Tifa then shows up and gives Cloud the light to defeat Sephiroth, and after more fighting, they disappear. Tifa then talks briefly to Sora before departing.

Now, I'm sure you've all heard that "if Sephiroth = darkness, then Tifa = light." Perhaps the connection between the three is that Sephiroth is actually the extracted darkness from Tifa's heart. Perhaps the light in her heart may have been so strong that it expelled all the darkness out of her heart, but unfortunately, it had the side effect of forming into Sephiroth, who feeds on the darkness in Cloud's heart.

Had Tifa appeared in the first game, and if she will appear in Kingdom Hearts III, I think her new outfit would be a derivative of her classic Final Fantasy VII attire, but with the addition of Rinoa Heartilly's white angel wings, to contrast with Sephiroth's single black angel wing and Cloud's single demon wing. And since her last name happens to be Lockhart, maybe that will tie in to her actually having a "locked heart," meaning that the Heartless cannot get her heart.