The plugin is not active while MAME is running -- only while MaLa is in control, so it's not the plugin's fault.
The issue you are having is with MAME and your U360s, not the MaLa plugin and your U360s. If your buttons work fine in-game with MAME then there is no reason that they shouldn't work fine in the remapping controls portion of MAME.
Good luck.