OK, this one's a bit of a stretch, but it's a possibility.
Consider that when Mother passes the protectorship to Jacob, she says, "We are the same." Then, when Jacob and Jack pass the protectorship, they both say, "Now, you are like me." Perhaps that's an indication that the powers aren't all transferred instantaneously. In other words, maybe Jack has some residual powers that allowed him to be immune to the Source for a little while, before he died.
I'm not saying that there's any clear evidence to support this, but it would be a workable answer to a question that many of us have.