I think Tim genuinely likes Alex as a fellow HM. I think he formed an opinion on the outside of the house before he went in that he really liked him. I also think he was well aware of the tide of public support that was turning for Alex. I don't find anything false about what he said to Alex through the bars last night. His reaction may have been confusing for Alex (as he's not sure quite what to think now, it is after all a game), but I think Timwas genuine in his comments. If anything, I think he may have been putting on a false front to his now fellow poor HMs as lets face it - he has to live with all 3 of them for the week. I see nothing wrong with this approach - when in Rome.
I think that Tim has believed from day 1 of entering the house that Alex is going to win, and apart from genuinely liking him, I think Tim also sees an opportunity to get in there with such a popular person and be there until the very end of the series (ie: final 4 or 3). At least I think that's what he's hoping for.
Being on a tv show such as this, you would want as much exposure as possible, for as long as possible, and I think by trying to make an ally out of Alex, who was already his fave contestant before he even entered the house, he is trying to secure a place to do just that.
Also: I think he has been trying to sending subliminal messages to Alex with all his gushing about how much he likes him. I don't think this is all about how much Tim likes Alex, I think Tim is trying to hint at how much support there is for Alex outside the house. I don't know if Alex is getting this or not, but Tim is certainly trying to let him know. At the end of the day, I think Tim knows he won't win, but everyone wants to be friends with a winner