I checked the link you provided and read the whole story, which is about Manny Pacquiao's deep faith in God. I'm sure that "calling on the advances" isn't an idiomatic expression at all in the context of his promoter Bobby Arum's statement. Instead, it's quite a literal statement--certainly not a figurative one--to the effect that Manny is always following up Bob by phone to check on the releases of the cash advances or down payments for his fights. Manny wants to get the funds as early as possible so he can meet the great demand for donations for various charitable causes, including those from religious groups.