The T8S ships with a ToneMatch power supply because the T8S cannot draw power from an L1 Model 1S or L1 Model II Power Stand.
You will need the ToneMatch power supply to power your T1 or T4S mixer when running with an L1 Classic, L1 Model I, L1 Compact, S1 Pro System or non-Bose equipment. You will need a one of these if you have two ToneMatch mixers running into a single L1® Model II or L1® Model 1S. — details below the picture.
If you are attaching two ToneMatch mixers to a single L1® Model II or L1 Model 1S then you will need this power supply to support the second ToneMatch mixer - the one connected to the Power Stand Analog Input.
See: Connecting Two T1®s to a Model II for details.