No, you force the JWT to be verified against the DB, which might be as simple as checking if the JWT creation time is older than the password update time in the DB, and if so, force only those users to log in.
All the token does is force some extra level of scrutiny. It doesn't mean the JWT has to be invalidated,but it does give you the ability to selectively invalidate specific ones for the cost of extra DB load once for all affected users.
Anyway, I'm still not convinced because when it comes to security I feel like it's a better idea to walk the well-trodden path, rather than invent new and exciting mechanisms. JWTs are useful for other stuff, but using them for security requires increasing back-end complexity quite a bit.
Sure, I'm not making a case JWT should be used, just that in the cases where the benefits it provides can yield real value (e.g. high capacity secured API with good caching infrastructure behind it), there are mitigations that might help offset the downsides.
All the token does is force some extra level of scrutiny. It doesn't mean the JWT has to be invalidated,but it does give you the ability to selectively invalidate specific ones for the cost of extra DB load once for all affected users.