The stare they shared was that of a man being confronted by his past. Not his daughter. He's been hiding and someone has shown up on his doorstep, which was very hidden information. Also he's surprised by the lightsaber as well.
Kylo has no recognition of her. It'd be highly improbable that they know each other. I can break down a timeline here for you.
Rey is abandoned at the age of five. She is approximately 20 now in the series. So she has been on Jakku for 15 years. Kylo is at most 30. Meaning that if Luke left Rey after the purge (the only logical time) then he would have been around 15. That's insanely young to the point that it does not make sense chronologically.
Furthermore, Rey is left with the junk dealer. If she had been left with the other guy at the beginning of the film then the idea would be plausible, but she was not. Luke, Leia or Han would have never left her with someone as slimey as the Junk dealer dude.
Kylo's focus on her is as a surprise (he knows who Finn, Poe, and BB-8 are but has no idea who "the girl" is), and potentially to do with his knowledge that the force has awakened and he might know it is in a girl. Simple as that.
There is nothing in the movie to link her to Luke. Nothing at all. In fact, if anything it screams of the opposite unless you read into the scene with Luke, but the obvious situation is the more likely one. That situation being that Luke is tired and he's being confronted with a past (the responsibility of the Jedi) and failure (its destruction) and he is weary to get involved again.
