The Influence Character throughline and the Overall Story throughline are two different perspectives in the story; two different contexts within which to solve problems. A player will host both the Influence Character in the IC throughline and an Overall Story character (such as the archetype of sidekick) in the Overall Story throughline. The context within which an Influence Character is driven differs from the context within which the Overall Story characters find their motivation.
So, we look to the IC Problem to see what is at work to drive the Influence Character. We look at the motivation elements in the Overall Story throughline to identify what drives the Overall Story characters.
What do you do about it? Nothing. When you are illustrating the IC Throughline, describe the IC's drive based on his or her problem element. When describing how the overall story character (the one that shares the same player as the IC) is driven, use the elements assigned in the Build Characters window (such as Faith).