No, using the same line as the remote turn on for your amps is not a problem.
How is the ITPS wired in? The white line should be the constant +12V line. The red is the switched ACC +12V line. This is how you have it setup correct? And then the small jumper on the ITPS goes to your power switch on your PC.
If your ITPS was only putting out .35 volt your computer would not even get to the bios startup screen. It would do nothing at all. It sounds like maybe you don't have everything hooked up correctly so double-check your wiring.