The capacitor plate connected to the positive end of the power supply would never pick up more electrons — in fact, it actually gives up electrons to the positive power supply, and that’s how the plate becomes positively charged itself.
But, as shown in the video, if you then flip that power supply around, you now have the negative end of the power supply connected to the positively charged plate of the capacitor. That positively charged plate is going to quickly soak up all the electrons it can handle from the power supply.
At the same time, the plate that had become negatively charged before the power supply was flipped will give up all those extra electrons to the positive power supply, until it becomes positively charged itself.
Let me know if it still doesn’t make sense.