Thaos becomes aware of your presence as a Wacther in the Sanitarium. Nobody is supposed to know he was there, and was doing a very good job at blending in. That was until you looked at him a little too deeply that he noticed you were a watcher.
As for Lady Webb, I don't think Thaos was letting Webb into his thoughts. From what was presented in the game I got the impression that Webb was able to break through on her own not because Thaos wanted her to see but because of her own will.