Assuming the hoses align with the color codes on them, then yes, both are pulling from same tank. But your logic is flawed the valves are not tied to a tank. Each valve has a hose to each tank, and the middle one is the one which goes to the engine. It would be more accurate to say that the left valve is for one engine, and the right valve is for the other - exact port or starboard TBD based on hose routing downstream of valve.
Switch one valve to the other side, and it will pull from the other tank.
BTW - thank you for following up with pictures. Was curious as to what you were working with.