When using my PS3 controller as a gamepad, how can I turn it off properly?

I managed to find something that works for me, and it appears that the answer was right under my nose. The DS3 tool's main window has a "disconnect" button, as can be seen here on the lower left:

As long as I make sure to press it before shutting down my computer, the controller stays dormant and doesn't bother my PS3.

If you reset the PS3 controller then it should no longer be synced with your PS3, and won't cause your PS3 to turn on.

You can use a paperclip or similar object to gently press the reset button.

Hold the PS button till the lights go off, instead of disconnecting