The browser extension indicates the time of the last sync under Settings > Sync. As a new user I have observed this occurring automatically when the database is changed, but haven’t witnessed it often enough yet to be sure it happens regularly.
You have? How quickly since the last update? Platform?
According to this explanation from Github from 2016, at least the Chrome extension polls the server every 6 hours.
The extension with poll the server every 6 hours for new updates. We could reduce the polling to a shorter interval but that would lead to a lot of unnecessary traffic to the server (since 99% of polls will result in no changes). The decision for 6 hours was to try and keep traffic down and give you the latest updates 4 times per day. If you made a change that you know you need and it is not listed you can simply go to the settings tab and do a manual sync.
Perhaps this has changed since, but in any case, the syncing isn’t automatic, hence it is poll updating instead of push updating.