You would connect the adapter to the input for the power, and the daisy chain plugs into the output to the other pedals. I use a 1.7A power supply with my NS2 or LS2 for 11 other pedals and have no smoke or explosions, yet
9 volts AC or DC? You need to get this one right - if you feed your pedals 9vAC, they will blow.
Boss has at times said you shouldn't run more than 200mA through the power jacks on the TU-2 - the two jacks are connected via relatively thin circuit board traces, which may lift if they overheat. But there's probably quite a bit of wiggle room there, and the total current draw for the pedal chain you're proposing comes in at just below 200mA.