Are you swapping and moving around the ~/.config/joplin/database.sqlite and files in that directory? Said another way, what's getting sync'd from the other computers?
I was doing similar, but each Joplin was File System Sync'ing to a second directory that was then sync'd with other devices via syncthing.
I've got 2 Windows boxes, and a Linux box (Elementary OS which is a Ubuntu base).
Resilio Sync synchronizes the files to each of the machine's local hard drive.
The 2 Windows boxes see the files just fine. As a matter of fact, I don't even have to synchronize for new content to show up as demonstrated by a test this morning.
The Linux box refuses to play along.
Is this a permission thing? I've set the folder that the files in to be read-write to everyone in Linux.
Check the Linux Resilio config to ensure it's as you expect and moving files. I assume you have a file manager - check to see that files are actually there.
Honestly, I'm not even sure how this would work, given a database is used by the application.
Here are a few other things to try (make sure you have a backup first!):
In the Joplin Linux client, create a new profile ("File" > "Switch profile" > "Create new profile") and try to set up sync.
If you would prefer to not create a new profile, "delete local data and re-download from sync target" may also work (though, as titled, it "deletes local data"). To use it, go to Options > Synchronization > Show Advanced Settings, then click "Delete local data and re-download from sync target".