Philip assumed she wanted reassurance and gave it to her. Elizabeth's response that she was a 'fast learner' seemed to imply a lingering anxiety. As was her bringing it up in the first place (as presumably the easiest problem).

I was so taken aback during that exchange - not by Elizabeth lying to Philip but by Philip seeming so at ease with the idea of Paige being involved in the spy business at all.

I accept this could well be because I didn't have time to rewatch season 5 and can't remember how the conversation between Philip and Elizabeth about Paige ended then.