If Tully has a relaxed relationship when it comes to flirting or pashing other people then that's fine, I certainly don't have an issue with it.
I understand she's the type that needs emotional reassurance but it's as if she's discovered that being in BB is a wonder-world of physical and emotional contact, and she's gone off like a pre-diabetic kid in a candy store. Not only is it obvious and outré behaviour, it makes her come across as fake. When Tully first entered the house I immediately liked her, but now it's got to the stage where almost everything she does annoys me.
Her problem is she pushes the concept of bonding with HMs way, way too far. A typical example of this was during the Feast on last night's show when she started hanging off Matt while he talked about the emotional turmoil of being in Afghanistan. IRL I can't imagine anyone being comfortable with that sort of invasive behaviour.
Later Caleb was talking about his life as a firey when Tully piped in with a toast to all the firemen, soldiers and everyone who provides dangerous services and I immediately thought Oh, for God's sake! It's the sort of comment you'd expect a politician to come out with, but from Tully it just seemed needy and fake. I'm not saying it absolutely was either of those, for all I know it was a genuine, heartfelt gesture, but it's a reflection of how her emotional neediness has effected my perception of her actions and motives. I pretty sure someone else here has said it, but it sums her up perfectly: she's a succubus.