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.
I also believe that the Ba'ku shown in 'Insurrection' had their First Contact with Picard. Whilst the Federation was aware of their presence, there was no contact until Data was revealed to them, and even then their true identities were not revealed until their interactions with Picard.
In regards to some of the other points made, as I understand it, 'First Contact' is proper, formal diplomatic contact between the Federation and another nation state. It is certainly possible for the Federation to be aware of other species but not to have made formal First Contact as of yet.
This also provides a convenient method for species to appear in prequel series or flashbacks prior to formal First Contact occuring. Whilst I didn't agree with all the appearances on such species on Enterprise, I do appreciate the logic of the formal First Contact process.
My thanks to those that posted in this thread.