I’m a bit confused about your question, because your title is asking how to move a T200 with a Thruster Commander, but then your main post says you’re able to move it with your Thruster Commander but not able to move it with an Arduino.
Are you attempting to connect the Arduino output to the Thruster Commander input?
The ESC takes a 1100-1900us pulse duration PWM input. The Thruster Commander uses the potentiometers as voltage dividers, which it reads and converts to the relevant PWM output that gets sent to the ESC. If you want to use an Arduino that should be instead of the Thruster Commander, not together with it (e.g. the Arduino output signal should be connected directly to the (white) ESC input signal wire, and the (black) ESC ground wire should be connected to one of the Arduino’s ground/GND pins.
Each thruster should beep 5 times on startup. The first three (rising in pitch) beeps occur when the ESC gains power, and indicate that each phase of the motor is connected. The next two (low then high) occur when the ESC gets a valid “stopped” signal, and indicate it is initialised and ready to start spinning on command. If you’re interested there are more details in the ESC product page, in the firmware manual in the Technical Details tab, and in Quick Start steps in the Learn tab.