I'm not familiar with Time Warner... so take this with a grain of salt.

You may run into two different problems.

Is the switched outlet on the cable box setup to "Switch"? I've seen them setup to stay on, no matter what the menu says.

You're going to have to plug a 12 volt transformer (Wall-wort) into that switched outlet. Most of the wall-worts I've dealt with take several seconds (up to 15) to de energize. This will cause a fault if the customer turns off, then tries to turn on quickly... the power supply will still be hot even though the cable box is off.