Additional buttons do not work in virtual machine.
Parallels Desktop emulates generic standard Mouse device with 2 buttons and a wheel, also known as a wheel mouse or a scroll mouse.
So, if you have a mouse with extended functionality on the Mac side, it will be impossible to use additional buttons or scrolling wheels in virtual machine.
Try to use 3rd party Mac pref pane called Steer Mouse that allows to program mouse features for any number of applications. Please open it, select Parallels Desktop and program the needful buttons by using the Windows shortcuts.