Kozinski wasn't with Starfleet. Though I'd imagine that the Traveler likely did interact with Starfleet officers prior to coming aboard the Enterprise due to being Kozinski's assistant.
As I recall, the Traveller was travelling incognito with Kozinski. I think they knew what he was capable of, but not who he was.
It was only during the warp experiments that his true identiy was disclosed to Picard. As such, I believe that Picard should be credited with the true 'First Contact' between the Federation and the Traveller species.
What we know of the Traveler from the show is that he's from Tau Alpha C, which was a world known to Commander Riker by the time the Traveler had beamed aboard. We don't know if Starfleet made contact with the people of that world, but they seemed okay with appointing him Kozinski's assistant and he apparently had a security clearance high enough to work with the engines of the Federation flagship. One can reasonably assume that Starfleet had already spoken with at least one member of that species, namely the Traveler.
Whether there was an official first contact is not known, but it's a reasonable assumption that Starfleet already made contact with Tau Alpha C. There's nothing to suggest that the Traveler is a separate species from everyone else residing in that system, but rather a member of that species who has learned to transcend space and time just as Wesley, a human from Earth, was able to.