Donnie Brasco, an associate, paid a percentage of his money he made to Lefty Rugierro, a soldier. He works directly for Lefty. I'm in the middle of his book and now Sonny Black, a capo, offers him to work directly for him, without first contact Lefty, his (former) mentor.

But Henry Hill, also an associate, paid a percentage to Paulie Vario, a capo. He works directly for him. Why didn't Hill have a soldier as mentor were he works for, like Donnie Brasco? Why did he worked directly for a capo?

When is an associate allowed to work for a capo (and not for a soldier)?

Is it not because Henry Hill was making a lot more money than Donnie Brasco!
Donnie was not trying to make profits for the mob he was trying to infiltrate them...whereas Henry was truly trying to make his way in the life at that time.
So simply because of all the money he pulled in & the fact that he started "working" at a cabstand owned by Vario meant that Vario had him as his man from the start!
All boils down to greed in the end!

Absolutely right!
Also, Juventus, you are assuming that there are hard-and-fast rules in the Mafia about who can work for whom. In general, a made man (a soldier) will be assigned to a crew. His crew chief will collect a percentage of his earnings, keep some for himself, and kick some "upstairs" to his capo. But an associate, becaue he is not "made," is like a free-lance operator--he can work for anyone who brings him into the Mafia family's business.
SPOILER:
One of the most exciting chapters in the book, "Donnie Brasco," is his description of a four-day "sitdown" in which Lefty Ruggiero and Tony Mirra argued over who "owned" Brasco and was entitled to a share of his earnings.