I also had to figure this out a few weeks ago when I lost my Mala setup due to file corruption and decided to rebuild my cab... it's very frustrating when you KNOW you researched the heck out of this stuff a few years ago, but now can't remember! :-)
While you can use the Mala fatfingers plugin (which I installed and then uninstalled a few weeks ago when I looked into this again) I then remembered that most people (including myself back in 2009...) set their U360 for "analog" mode when launching MAME and use MAME's built-in joystick mapping.
So in Mala under the "Controller" main-tab, "Encoder" sub-tab, I've pointed "Encoder software" to UltraMap.exe, and set "Default Config (MaLa)" to the 4-way ugc file. Then under the "MAME Config" main-tab, "Encoder" sub-tab I've pointed the file box to the analog ugc file.
You also have to set "joystick 1" in your mame.ini file to enable the joystick.