Alternatively, we could argue that, as the applied field becomes bigger, more radiation is emitted in a direction which is not along the spin direction (upper or lower hyperfine level), so that would mean that more nuclei (or atoms because states of entire system?) in the ensemble can jump to an other hyperfine level. This could be because that hyperfine splitting is smaller (smaller energy bridge to cross). The reason for that smaller splitting could be because of an antiparallel direction of applied field and hyperfine field. The applied fields are positive, so the hyperfine field would be negative then.
I am not sure which way of thinking would be better.