They were still used in circulation. They just didn't mint new coins in their predecessors way. They minted their own new coins.

Unless the throne was usurped, normally emperors would start their coinage by depicting their predecessors face on one side and theirs on the other, or whoever else shared power with them. Usurpers would usually use coins to try to link their line with an older imperial line, to try to gain legitimacy. That said, if I recall correctly the Flavians did not do this, but most other emperors who were not of the previous dynasty did through one way or another.