When the burners shut off after the thermostat set temperature is satisfied, then the entire furnace should shut off except the main blower may continue to run for 30 more seconds. The behavior of the inducer isn't right.
The first question is are you certain the thermostat set temperature has been reached when the burners shut off?
If the answer is yes, then either the thermostat may be sending heat requests intermittently (not likely) or the control board is flaky. You can try the following test to determine a bad thermostat.
Turn off the power to the furnace. At the furnace control board disconnect the W wire and tape the bare end. Now with a short piece of insulated wire you're going to jumper the W and R terminals. First, you can connect one end of the wire to the W and then you will touch the other end to the R.
Now with the furnace power on, touch the jumper wire to the R terminal. There may be a small spark but hold the wire firmly... it's only 25 volts. The furnace will start as it always has. Let the furnace run and after the burners have been on for a minute and all seems stable, remove the wire you've been holding from the R terminal. The furnace will now shut off. If the inducer still behaves in that previously odd manner, carefully check the control board for any signs of heat damage or cold solder joints.
Be sure to turn off the furnace before reconnecting the W wire from the thermostat to the control board.