Tino adores one of his friends, that is true. (In fact, when Tino said Nee-sama, she's referring to that friend)
Her calling him master was never explained early on, just that since he's a friend with her onee-sama, she call him master.
iirc his friends basically leave the decision on whether to let Tino join SG up to him, and he basically told her he'll let her join when she's strong enough.