OP's question is deceptively simple yet very thought-provoking, and I have yet to see a good response.
Basically, I'd say OP, that "alphas" are men who, in general, do what they
want to do. Betas are men who do what they
have to do.
So, to answer the question of whether providing for others is, ipso facto, beta, we'd have to answer just
why exactly the specific man is doing the providing.
If it's because he (for some reason) wants to, then I see no reason why providing couldn't be an "alpha" activity. However, if he's providing because he feels that it's his duty, it's what society wants, or because that's what will get him a hot chick, then that's beta.
I am skeptical about "providers" being anything other than beta simply because I personally have never wanted to provide for a woman, children, or anyone else. I like to spend my resources on my own desires, thank you very much.
But, I'm not categorically opposed to the concept of a "provider alpha." He would have to be ruthlessly honest with himself about why, really, he's giving up his resources to creatures that are not him.
I think a lot of men believe that if they create things that will last beyond their lives -- such as children or works of art or monuments or ideas or whatever -- that doing so will somehow confer some level of immortality upon them personally. In that case I could see how "providing" to achieve some sort of legacy would be beneficial for them.
However, I don't have that view of existence. I believe that, when I die, everything is over forever. That's just my metaphysical view. Therefore, for me, giving money to others would
always necessarily come from a "have to" perspective and would therefore always be beta. Like a poster above me said, I think humans' drive toward creating "legacies" is part deep-seated, probably genetic terror of death and part social force. I consider myself enlightened to realize, like Tyler Durden said in Fight Club, "Know -- don't fear -- know, that some day you're going to die."
I do fear it, but I think I know it better than a lot of people