I do not own this unit. At a glance, those switches appear to save the owner from using jumpers to make a series or parallel connection between CH1 and CH2. In parallel, be aware of the rated current of the switch [ in theory, the device can deliver 10A] and in series the Vdc output isolation breakdown voltage; in series its unlikely to be an issue since the maximum series Vdc this devices outputs is <= 60-65Vdc.
For either mode to work, both CH must be isolated from each other and you do not earth any terminals.
Some problems: if you earth the neg terminal of both CH, you will short out CH1. In parallel mode, it should not cause DC problems, but you have a shock hazard in higher Vdc as earth ground is chassis ground of many appliances as well as DSOs: if you touched the pos terminal the circuit completes using earth if you touch anything earthed. Earthing the neg terminal would also allow a path to receive RFI, and other common mode noise sources, into your power supply line.
You cannot use earth as a reference for a neg and pos supply because it will not form a full circuit. You can put the PSU in series mode and use CH1 + as ground and split the supply.