Alan was pretty pissed when he came out of the Jensen estate, so pissed that he actually lost his mind in the process! Gradually, the combination of the humiliation he felt and his shameful defeat pierced his heart. If he did not make Alex pay for all this, he might go insane. The other source of his anger was the way the Jensen family treated him! Sure, they were a powerful family, but he could not let them make fun of him like that.
He realised that Alex and Eliott already knew each other, and she had certainly made up her mind about him before he had even contacted her. He realised he could not let her go that easily, they had cheated him and taken his 15% stock, plus his only income at the moment, if he did not let them pay him he fear he would die from anger.