Given her contempt for Danni so far, I suspect that Ulani is liable to let things slip anyway. It might be better to hear it first-hand.
I'm surprised she says "it's not some big secret" after earlier making Loki promise not to let it get back to the school. Unless there's something else...?
I think she means it's not a big secret in the village, maybe.
She says it's not a huge secret but also doesn't want people she doesn't know real well to know about it... so she may be downplaying it to get Loki off her back :P