The Basiji are volunteers. They are not paid, but are provided with some basic things like transport and clothes. Their duties are comparable to the National Guard in the US. They are called up when needed. They do security work for the govt - thus fighting protestors - but also more ordinary work such as digging up after earthquakes. They are usually young working class men with few employment options. Service as a basiji gives them the possibility of later on getting a paid position in the Revolutionary Guards, and other govt corps.
What you have stated is partially true. But from back when these protests first began, the regime began importing foreign thugs who are the “new” Basij. That is why they are so hard to get a handle on.