See the eM Client Quick Notes support blog on how it works.
Quick notes in search results? - Mail - eM Client
Also see eM Client forum thread below
Sync email notes - Mail - eM Client
@Gary post from the above thread.
It doesn’t sync through IMAP. It does through EWS though, so if you have the same account setup as Exchange on two devices using eM Client, the notes on the messages will sync.