This is from before the full truth of the echoes is revealed:
Later in the game, with the echoes stuff (Jedi Council/subsequent encounters) it is explained more about what your effect is on the Force and others around you.
Ok, so this is a bit misleading since the person recording has removed all context from the conversation. Listening to it this way could lead one to believe that Kreia is saying that their willingness to follow is based on some power you have.
The fact is she states at least a few times that they do it because you are a leader, you represent to them something either worth being or fighting against.
The key word here is either, proving they have agency in how to respond to your presence. The one going around using the force to manipulate people is Kreia, it could be argued certain members only follow you becaause of her, such as the Wookie, Hanhar.
The only concern the council ever had was that you were a parasite, leeching the force from every being you come in contact with. Both Kreia and the council believe this, this is why the council wants to destroy you and conversely why Kreia wants to preserve you. Neither of them really care for or about your allies. Kreia is the only one who is seemingly contentious about them and not because you are force-breaking their will or anything like that, but simply because they might disuade you from being her perfect puppet or figuring out what Kreia is truly about before she is ready to reveal it.
Edit: Ok, so this isn't directly mentioned in this game but I think I know what you're getting at Rean:
So, both Kreia and the Council believe the Exile to be a wound in the force, parasitically sucking the force out of others, and that this could result in the "death of the force". The truth ends up being that you suppressed your own force abilities after Malachor V and went into hiding. You do still carry the echos of everything that happened during the Mandalorian Wars and it's this that causes the Council and Kreia to see you as a wound. You are able to reawaken your force powers because of force bonding, a usually very difficult technique to even pull off once, but something the Exile not only does easily, but to almost everyone they come across, and all subconsciously. It is very likely the force bond could be manipulating your allies, the same way Revan is able to use it to save/turn Bastilla in the first game.