To me Tim doesn't strike me as an alpha type so I wouldn't call him that. However he did fall on that 'role' in the house once, as you said, the 'cool kids' realised their perception of the house dynamics did not match that of the outside voting viewers.
It was at that point that there was a 'begrudging' fear and resentment against Tim for 'controlling' the game (i.e. Heidi turning against him for no good apparent reason, jealousy was probably where it mostly stemmed from).
They knew he was made out of Teflon and had to be careful how they interacted with him as by that stage they had figured out Tim was a favourite on the outside evidenced by the the fact that anybody who a 'confrontation' came out second best via being voted out. Hence why Ed started the half cocked 'smear' campaign against Tim that inevitably was to no avail.
Yeah I don't actually see him as the traditional alpha male in that sense, but for the debate in this thread, I wasn't sure how to categorise him either. So for arguments sake I say alpha male.
The problem with ed remaining in the house was that some of the hms then categorized two divisions in the house- a good and bad side. this was championed by the hms who perceived ed as the good, and when he was gone and footage released of him putting jade up, it was then that jade realized that maybe the good side was always with Tim. I say maybe because she still needed to talk to ed about what happened before actually giving up on him. So basically ed was still considered in a way the alpha male, up until his eviction, and it was then that Tim was seen as 'alpha male'.