Hi Ryan,
It might be that the WP Rocket is showing you old cached page when the plugin is enabled.
Please clear the WP Rocket cache and check it out.
Announcer works in a very simple way. So when WP rocket caches the page, it should contain the announcer plugin working on it. This way the page will cache along with announcer.
If you notice the issue again, please see if you need to reconfigure WP Rocket settings. If issue persists, please send me the page URL where it is not seen.
Thanks,
Aakash