I disagree somewhat...
Series or parallel does make a difference regards the maximum available voltage from the battery and hence the internal circuitry. Although I do take the point that there are sufficient protections to stop your battery exploding.
Power is controlled via modifying the voltage, typically by a buck converter or equivalent (when downrating the voltage)
This effectively consists of an inductor, diode, transistor switch and capacitor. The transistor switches the voltage on/off with the capacitor smoothing out the PD. The other components prevent too high a current from charging the capacitor/prevent flow back through the batteries.
As you increase power you increase voltage and because V=IR, and resistance is fixed (we’ll not consider TC in this example), current also increases.
In a series circuit potential difference is additive, but current through all the cells is the same. As such it is possible to draw more current through the cells than the maximum rated continuous discharge.
Your mod does not know what the rating of the cells is. It will just switch off if it detects a problem with the cells. It is good practise, even in a regulated mod to be aware of battery safety and maintain a continuous discharge below the rating of the cells