Link does not need to be told twice.

Immediately, he scrambles right back up - which might involve another leap, depending on how high Hajime is right now. Only then, when he's back on Hajime's back, does he stop and realise that the only people he gave gifts to were people. The reindeer's voice is familiar too, isn't it?

"... How are you a deer?" he asks, because Link had not realised that turning into a deer was something someone could just do.