You are not considered your own teammate for this purpose. (EDIT: Oh. That was meant for Noon, not for you. Then I noticed Noon didn't have you and forgot I'd put that there already)
If it says "give influence to...", it means they get influence over you. It's actually quite clear. <.< But I've played other systems based on AW before, so I recognize the wording, which hasn't really changed other than "Influence" vs something like "a string"...and strings were far more confusing.