Be it with SDK 3.0.6 or 3.0.8 and the ConnectIQ Eclipse Plugin 3.0.6 (in Eclipse 2018-12), the App Settings Editor does not work on Linux. Application.AppBase.onSettingsChanged() is correctly called but Application.Properties.getValue() keeps returning the default values.
By looking at the ${TMPDIR}/GARMIN/APPS/SETTINGS folder, I found the culprit might be case-sensitiveness of Linux and the fact that the <APP>.SET file (uppercase extension) created at the time the project is run in the simulator does not match the <APP>.set file (lowercase extension) that gets created/updated when the settings are sent (allegedly successfully) from the App Settings Editor.
By deleting the <APP>.set file and hard-linking it to the <APP>.SET file (ln <APP>.SET <APP>.set), properties *do* get updated as expected, reflecting the change made in the App Settings Editor.