Well My TIU is powered with an extra 12 volt DC power adapter that I had in the parts drawer. These can bought online for around 10 bucks or so. Just make sure that you get one that is rated for 1.5 or more amps (in case you decide to and an AIU later on). But Arnold's z500 brick also works. Th AUX power port on the TIU is not picky, just keeps the volts to 21 or less.
My TIU Aux power supply turns on and off with everything else on my layout, I don't see the need to always leave the TIU powered up if everything else is powered down. My who layout is plugged into a nice power strip that provides me with a master switch or one can opt to get one of those remote control outlets so that all of your power can be hidden under the layout and turned one and off with a small dedicated remote control button.