Tension control using a DC motor
The motor will not create a large back EMF unless the motor is rotated rapidly against the torque. If that is the intention, the controller would need to be designed to dissipate the regenerated power or return it to the source. It there is only a slow movement, the power will be dissipated as losses in the motor.

Torque control is achieved by controlling the armature current. For a set torque, the current will be relatively constant. The PI or PID control will adjust the current a relatively small amount to compensate for changes that occur in the system. The primary change will be the increase in rotor resistance as the rotor temperature increases. If the wire is allowed to be pulled out or rewound rapidly, the control will need to be more complex. You may need an overriding speed limit control.

At this point, you have not completely and accurately described everything that you want to do. I don't think you have asked all of the right questions.