Okta "The client specified not to prompt, but the user is not logged in"

Access to the OIDC app is no longer dependent on the Okta session when you use refresh tokens. If the refresh token is being used, the Okta session expiring after 12 hours will not affect the users access to the application, only the refresh token lifetimes will matter.

So no, you should not see the users getting logged out after 12 hours provided your app is receiving and using the refresh tokens instead (you can check if it is by confirming in the browser that, upon token expiration, you only see requests to the /token endpoint (with the refresh token in the body) and there are no further requests to /authorize after the initial login.