Alex wants a tv career, his persona is "dr Alex" as he even calls himself on his own Twitter account. He used Alexandra, he should not have got back with her as he knew he wasn't interested when he did.
He was busted. That was it basically. The other islanders were already talking about his behaviour, the difference between his words and actions. So it was clearly very obvious. He went on that date and lied through his teeth to her, saying he saw a future outside etc, wanted to see her, then came back and dumped her immediately.
If some folks think that's an ok way to treat someone then words fail me. For me it's wrong. He used her to play the game and was never interested.
We can speculate as to why he wasn't interested in her or arguably any other woman on that island, and why the woman all react to him as they do, but the bottom line is he lied through his teeth.
He also used grace, dropped the other woman he was showing interest in, he even asked them to switch who slept in his bed, when it was blatantly clear he had no interest in grace, and he gaslighted Ellie, when it was clear he had no interest in her either, and fought with eyal over Megan when his subsequent behaviour shows he's never been remotely interested in Megan either.
He's in there as a platform to get a tv career. He's not interested in any of the women, never has been and he's used them to stay in so he can get a shot at his tv career.
I seriously hope he doesn't get one.