Of course he used magic! What else could he have done???
Personally, I think it has more to do with his knowledge from his membership in the Psijics than his membership in the Telvanni. I hate to use a guess like that, but I personally see Psijics as a BIT more magically competent than the Telvanni.
It could very well be the simple idea that Fyr was quite a traveler and could have just picked the crap up on his own.
Well, the Telvanni tend to be very reckless, almost more of a mad/crazed scientist that wants to be left to his/her experiments. The Psijics seem more calm and collected, taking things more slowly, not so reckless, but more harmonious with the magicka around, but don't expect them to take any person in. And I'd say that Fyr's abilities may partly be from his Psijic training before, but I'd gander the majority of it would have to be his own experience, and his studies about the dwemer. But, the dwemer thing may be a recent activity he picked up a few hundred years ago. Also, he may be a Telvanni, but his membership is more like he is and is not, more like a very informal member. Even the other Telvanni council members see his membership as a very informal association.