At first the interface (DB9 to USB) must support the third button and scroll wheel. If it does not, there is no way to get it work.
If the interface supports the middle button, it should work out of the box. But of course you need some software like FreeWheel which allows you to assign a function to the third button. AmigaOS as such has no use for a third button.
For the scroll wheel an additional driver is needed. The driver should have been included with the interface. If there was no driver included, then most probably it does not support the wheel.
If it supports the wheel and the driver is running, you need again some software which allows to assign a function to the wheel. Again FreeWheel is the most popular choice.