Why doe my a/c blower motor run even when the thermostat is set to off?

Are you talking about your outside condenser motor or the inside air handler motor? With the t'stat off, you can still run the fan if it is set to ON. Where is yours set?

Are you talking about your outside condenser motor or the inside air handler motor? With the t'stat off, you can still run the fan if it is set to ON. Where is yours set?

It is the air handler blower motor and the stat is off and the fan is at auto

Some units have a delay for the blower to run a little longer after thermostat is turned off.