I think this whole testing has a different background than just the change from beta to alpha. It has to do with being the alpha.
As can be seen with animals that live a very alpha/beta hierarchy(for instance, packs of wolves), the alpha male is constantly being challenged by the others. This testing will be more severe with a new alpha as he still has to earn his respect. But in the end, even if he's an accepted alpha, he will be challenged and tested.
I see this happen constantly. At my dancing group I'm an accepted alpha as I've always behaved like this. Most people accept my place in the group(ie., the center of attention), but a few are kicking up dirt over me. One of the guys calls me Mr. Perfect and is trying to keep me away from a girl he is really into by talking crap about me and making arrangements with people who hang around with me to exclude. All they do is tell me about it and laugh at his expense.
All you have to do is keep your frame here. Act like that alpha, either by gradually introducing it or by just changing in 1 go. But once you did make the change, don't go back, or you'll loose all respect. As happens with the wolf that was once the pack leader and lost. Noone respects him, and he either falls to omega male(outcast) or gets killed.