The way I interpreted the last few scenes about Taeseo was that he was an "incomplete" alpha or just wasn't one, in the beginning. Since the doctor was prescribing him some meds to stabilize his Alpha side ( ̄へ ̄) if I had to guess or have a say in what's actually happening....he might've just been a late-bloomer as an omega.
But then again... it's omegaverse fiction╮( ̄▽ ̄)╭ the author's are free to make up the logic in their stories

how taeseo got pregnant even though he’s an alpha (i haven’t read the manhwa, just trying to clarify before i invest)