its probably an incompatability with your new powersupply. i had this once with a computer. your computer is in fact compleatly turning off but then when the computer requests periferal power to keep the clock running etc. it sends power that boots the entire computer (this is what i suspect anyways). it was happening to me like i said exaclty as you described. What i would do is use the little power switch on the back of the powersupply to keep the computer off if I needed to turn it off but most of the time i just let it run. the problem solved its self with a differnet brand powersupply.
1995 Talon Esi - 1989 Lebarron - 1991 Mr2 Turbo - 1991 Accord - 2005 Corolla - 2005 R6 - 1993 Talon Tsi - 2013 Mustang Coupe - 1997 Grand Prix GTP