There are undoubtedly similar reflexes that assist fulmars in learning to fly quickly, but that doesn't mean that rapid learning isn't also required.
As a baby I fell into a pool and needed to be rescued. I didn’t inhale water, but as generally happens I very much did just sank to the bottom. Babies can be taught to float at around 5 months, but it’s not reflexive.
I can't say what the extent of those swimming reflexes really is, but water births are not unheard of. Besides there's literally countless examples of this sort of thing, most prey animals can walk or even run mere moments after being born, cetaceans and ram ventilator sharks all know how to swim immediately or they would literally drown, insects can fly as soon as they hatch, etc.