How can a pot allow variable off times in a time delay relay
A analog timer uses a RC network to create the timer delay, where
$$T (seconds) = R (resistance\space in\space ohms) \times C (capacitance\space in\space farads).$$

So if the potentiometer controls the resistance, it will also control the time delay in a linear relationship.

This RC time constant is the amount of time the circuit takes to charge up to 63.2% of its final value.  A circuit will typically use some sort of comparator to compare this varying voltage to a fixed voltage, and end the "off" timing period.

In your case, there would be a second fixed resistor that controlled the "on" period (or the variable one might control the off period, and the other fixed one control the overall period, on+off).  The two resistors could share the same capacitor, or use separate capacitors, depending on the circuit.  It would toggle between the two using a flip-flop or equivalent.