What it is in ammonia that can trigger asthma?

Bronchial irritant. Ammonia can trigger asthma since it is a bronchial irritant. It is not a specific allergen. It is an asthma trigger in the same way that chlorine near a swimming pool or other strong cleaning agents can be--by irritating already "twitchy" or reactive airways.
Pungency. Any strong smell can trigger asthma - we don't allow perfume in our waiting room. Same goes for smoke, fumes and most cleaning detergents.