「Both of them share feelings for Cloud 」 — Tifa was close to Aerith, who can also be called a love rival.
I always thought this quote referred to Disc One of the game, when Aerith was still alive? Since Aerith was so straightforward in her feelings, Tifa did get jealous, yet at the same time, she was still Aerith's friend.
With that point in mind, they were also good friends. Nevertheless, it is not hard to imagine that she carries complex feelings as a woman toward Aerith, who had built up a special bond with Cloud that was different from Tifa’s.
Yes, because Aerith died - as Bella stated, guilt and all that jazz thrown in the mix, because well, Tifa *is* the one chosen by Cloud, after all. But if anything, this quote clarifies that Cloud and Aerith's relationship was never romantic.
Tifa’s complicated feelings continue even in AC, two years after Aerith had departed the world. This was due to the fact that Cloud, succumbing to the notion that Aerith’s death was his fault and condemning himself, construed that Denzel was “the child which Aerith brought here” and took care of him. In addition, Cloud had also gone away to the church that Aerith had been in. The thing which she is unable to hide in her irritation towards Cloud is the fact that he isn’t merely dragging the past around, but because that reason might perhaps be related to Aerith.
Contrarily to Bill, I do believe that there's a hint of jealousy in those complicated feelings, as well as guilt and friendship - she's wondering why Cloud is dragging the past around, IMHO. However, her jealousy is because Cloud seems to be chosing to drag the past around [and thus focuses on Aerith - and Zack for that matter, but she isn't aware of Zack] rather than chosing their family which upsets her. She knows why Cloud feels guilty, yet she can't be helped feeling pained by the fact that he's been hiding it all from her, when his family could bring him the support he needs.
That's why the bedroom scene in AC was so important to me; because not only it had that feeling of a woman telling her man to stop being an idiot, but also because it refocuses Cloud on his family and the problem they're facing. That the kids and HIS kids need him. That he's an idiot because they are supposed to be a family, and that she's been hurt by his behaviour. Because she scolds him, he is able to go and save them - and be forgiven by Aerith in the meantime.
As Cloud told Sephiroth, "there's nothing that's not important"; Tifa and the kids, Aerith, Zack, they all are special in his heart, all in different ways. And he will fight for them.