And it seems that, according to the WPSOLR indexing screen, the synchronizations can only be done manually and not via a WP filter/hook when a posts get updated.
I can confirm that your posts are indexed in real-time (unless you deactivated real-time indexing in screen 2.2).
But posts indexed in real-time appear also as “not indexed yet”. It is just a guarantee that they will be picked up by the next synchronisation, if the real-time event failed for any reason.
