you have the remote wire on the power input of the amp wired to a terminal on the power supply. it also looks like the amp ground is connected to the AC input ground, but not connected to the minus or common terminal on the output of the power supply. since such power supplies have floating outputs, the negative of common terminal of the supply is not connected to frame ground. this is why the amp doen't turn on. there should be a switch between the +12V terminal on the amp and the remote terminal, so you can use the switch to turn the amp on and off without having to plug and unplug the power supply . it might be helpful if we knew what the terminals on the power supply were labeled as.
you didn't mention the impedance of the tweeters, but that amp delivers 38W (per channel) into 4 ohm loads, and 75W/ch into 2 ohm loads (the specs should be listed in the owner's manual). the amp is a class AB amplifier, so that 22khz spec is probably the amp's natural rolloff characteristic.