Ilusioné comes from the verb ilusionar, meaning to fill with hope or to excite. In this context, it means "I got my hopes up" or "I became hopeful."
It's an interesting word because it captures the feeling of developing strong hopes or dreams, often with a hint of naivety or a romanticized view. The singer uses it to describe how he became hopeful about a girl after she looked at him, setting the stage for his eventual disappointment.
The whole bachata is one man reconstructing a romance that only ever happened on his side. He dates it back absurdly far — "El día en que yo nací" / "Vi una niña muy bella" (The day I was born / I saw a very beautiful girl) — and the evidence he actually builds on turns out to be a train ride at fifteen: "A su lado me senté" / "Y mi corazón saltaba" (I sat next to her / And my heart jumped), and from that, "Y hasta me llegué a creer" / "Que ella era mi enamorada" (And I even came to believe / That she was my girlfriend). He invites her home "Pensando que me quería" (Thinking that she loved me) and wants her to work it out for herself — "Y quería que adivinara" / "Lo que el corazón sentía" (And I wanted her to guess / What my heart felt). He never says it out loud. Her answer takes two lines: "Ella a mí me rechazó" / "Porque no me conocía" (She rejected me / Because she didn't know me).
That is the lie of the title, and the song leaves him still living inside it. The last third puts him back on the platform, "Esperando por mi amada" (Waiting for my beloved), with "Y no dejo de tomar" / "Hasta que no llegue ella" (And I don't stop drinking / Until she arrives). Meanwhile the band keeps playing around him — "Oye, chef" (Hey, chef), "Suénala, Mikey, suénala" (Play it, Mikey, play it) — a dance record cheerfully carrying on over a man who has not moved from the station in years.