Winston invited Jimmy up for tea just to chat, to figure out what exactly happened with the news, and there was nothing that required Jimmy's action.
It's actually related to Winston and their business. As an assassin group, they naturally operate in the dark. Jimmy is Winston's friend, not affiliated with the Continental Hotel or the High Table, so relatively speaking, he is safer.
If Jimmy were to become a public figure within the FBI, Winston would then have to prevent him from engaging in any shady operations, as it would risk exposing their connection, making it a hassle to clean up.
Jimmy hadn't really considered that this might affect Winston, given that he had never had public figure experience. Although he had dealt with many cases, for protection purposes, his identity was never disclosed in related task briefs or public videos.
