I believe if you download from plex.tv and manually install then you’ll have to manually upgrade when new releases are available.
The process is easy. It takes all of 2 minutes on my DS918+ - Stop, Uninstall, Install New, Start. No data/metadata/etc is lost/changed/etc.
You can subscribe to the Plex Media Server announcement thread to receive e-mails when a new version is available. Scroll to the bottom of the thread and change Normal to Watching.
I don’t remember how auto-update works with Synology Package Center. I haven’t used it in years. I’ve been burned too many times by buggy Synology updates. I always wait at least a week before installing any Synology updates, whether OS or applications. In the past Synology has published OS updates that have been incompatible with Plex and Hyperbackup updates that have irretrievably trashed backups.
Since I don’t use auto updates for Synology packages I don’t do it for Plex. Habit more than anything. I’m not sure if you can auto-update some apps but not others.