He is not a UFA. He is an RFA. There is a difference.
The Jets qualified him. So he is still property of the Jets. He can choose to go play in Europe if he wants. But he will remain property of the Jets.
Puljujarvi left for Europe when he was an RFA. He was still property of the Oilers.
Habs qualified Leskinen last year, so they retained his rights, even if he went to play in Europe. He came back and at the moment he was signed by the Habs, he could ONLY sign with Montreal. The only way he would have been able to sign with another team was if Habs didn't qualify him this year, which would make him a UFA and he can sign with any team he wants.
What you're talking about Jets matching is if he is tendered an offer sheet. But Jets get the opportunity to match because as I said, he is property of the Jets.