so either way the potentiometer controls the speed no matter the motor?
Until you give the DC motor more voltage than it can handle... then there is smoke and no speed.
But that is limited by your input voltage.
Keep your input at or under the Volt rating on your DC motor and you will be fine.
When you under voltage a DC motor the torque (on most motors) will drop off tremendously. You will notice this when the motor is under load. This application of spinning a spoon in water requires little to no torque so it isn't an issue in this case.
You can get around the torque drop off by electronically pulsing the DC motor at full voltage though the use of an electronic speed controller (trolling motors and RC cars use these), but that is a lot more expensive and not needed in this application.
Generally speaking you won’t hurt a DC motor by undervolting it. Its torque and speed will diminish until it has too few volts and it just won’t spin.
Keep your input voltage at or under the motors rating and the top end is taken care of too.
AC motors are different they require constant voltage.