How to correctly supply power to multiple 12 V devices wired in parallel?
The Peltier tiles consume a lot of power, and it sounds like you have no measuring equipment (multimeter) nor datasheets for the device. 

It's safe to assume the tile alone consumes just about everything that your fixed power supply is rated for. I wonder how/if your adjustable power supply measures the voltage level when you set it or if it's just a knob with divisions and no indicator - in which case when you set the knob to 19V you are likely getting closer to the 12V you need to run everything.