I wasted too many cycles trying to understand how it was secure while debating how much latency my database check was introducing on every single request compared to those simply using the JWT as-is.
It has made something I considered "settled" to be a time-sink.
(Nb. I've not personally seen them used in a case for which they make sense, yet, but only in smaller projects because they're trendy)
Another thing one must be aware of with JWTs is protecting your users against XSS and CSRF's. Make sure your shortlived token is stored on localStorage and the refresh one is stored in a cookie.
Unless you mean blacklisting tokens, then, yes, you do need to check your blacklist, though fanning that out to an edge cache should suffice and keep you from needing to hit your authentication service or database every request. But that's true for any long-lived session token.
With stateful authentication, solving this is trivial: just check your tokens/sessions/whatever against a centralized database every request.