1) Pedals that use reverse polarity are NOT simply reversing the tip and shaft of a plug. Imagine a bipolar power supply with +9 and -9VDC. "Regular" pedals only use the +9 "side" of that. Reverse polarity pedals only use the negative side, but share the same ground, such that any power plug going into them would be tip-ground and shaft-negative.
2) I'll repeat the advisory that pedals including a clock of any sort should be run off their own isolated power source. Why? Clocks will put spikes on the power line. When spikes from one pedal encounter spikes from another, they can (which is not the same as will) produce what is called "heterodyning" - an outcome which can be summarized as being like ring modulation. Older digital pedals are susceptible to this. The story would typically go like this. Player has a digital pedal that runs nice and quiet. They go to a store, try out another digital pedal, that runs just as quietly, buy it, bring it home, plug it in on a power source shared with the first pedal, and encounter a wasp's nest of noise and buzzing, prompting them to return the pedal as "broken" or otherwise malfunctioning.
The commonness of such outcomes has led to manufacturers building protections against such outcomes into their pedals AND power supplies. Sixty years ago, the same things would happen in homes. The power line your home's washing machine, refrigerator, sewing machine, air conditioner, and all your dad's power tools plugged into, was shared with the radio, stereo, TV, and your guitar amp. If a motor anywhere in the house was turned on, all audio and TV reception went to shit because of spikes on the shared power line. As time went on, more appliances became designed to prevent susceptibility to power-line spikes going out or coming in, and I imagine home power also became a little more isolated.