A typical use of the power supply schematic in the O.P. is for powering one (1) analog circuit, which needs both positive and negative power supply rails. In principle, you can power two (2) completely independent circuits from it (+9 to 0 and 0 to -9). This would be a peculiar scheme, though, because the ground of one circuit is at 9V (plus or minus) w.r.t. ground of the other one. Still, if the circuits are in fact independent, such scheme would work. In practice, this scheme is not used in general purpose desktop power supplies.
A classic desktop power supply (like the one in the YouTube video linked in the O.P.) is of a "dual positive type". Each channel has its own independent secondary winding (or even a separate transformer) and its own rectifier. The channels can float with respect to each-other, and that allows to connect them in series.
Just because the continuity test function of your meter does not detect a short does not mean there is an unintended path for excessive current between the supply rails. There are many potential faults that could exist but won't be detected with a meter like that, but here's one: a forward-biased diode between the rails.
Most meters, except the very cheapest of them, test continuity with less than 0.6V precisely so that they can't forward-bias a silicon P-N junction. Thus, they will not detect a diode as "continuity" regardless of which way you place the diode with respect to the meter. However, to any power supply significantly more than 0.6V, the diode might as well be a dead short, if it's forward-biased.
If your circuit is simple, the easiest way to troubleshoot is usually to inspect it very carefully, looking for errors. If that fails, you can connect the power supply and leave it in CC mode, with the current set low enough that you aren't burning anything. Then, with a good, precise voltmeter, start measuring the voltage drop between points on your board. Where there is a voltage drop, there is high current (remember, \$E=IR\$), and thus you know the fault is somewhere between those two points. Be methodical about it and you should be able to find the fault by process of elimination.
Best Answer
You should wire the power supply like above picture. Put both 30V channels to 12V. Then connect them in series. The wire connecting the - to the + is your reference.
I think you are confusing the ground with your reference voltage. Ground is attached to the wall plug of the power supply which is not the same as your reference voltage.