After reading of problems with this gadget including power supply suitability, temperature-dependence etc. and having landed one on my bench to “fix” I have the following information which should clear a few things up.
The problem with the unit I was given is a pitch variation which should not be present for a straight delay setting. Without analyzing the circuit in depth (don’t have a schematic) I infer the following: the timing oscillator is an R-C type whose frequency is supply-voltage and temperature dependent. The correct type of plug pack to use is a regulated one (i.e. a switchmode type). Normal unregulated plugpacks will not give correct results as there is ripple present in the output. I inferred this from observing that the unit worked correctly on battery (which is effectively regulated and smoothed). The company should have built a voltage regulator into the unit. Not doing so also means that the delay period will change as the battery is drained.