You are partially correct.
The machine not the (wired or wireless) remote or timer controls the reheat cycle.
When the heated tube is unacceptably below operating temp a thermal switch located on the tube assembly diverts power from the light on the remote and the fluid pump.
As I recall the lights are just wired in parallel with the pump, so when power again becomes routed to the pump, the light on the remote tells you the machine will run the pump if you close the switch on the remote. Look a the threads and articles covering triggering the fog machine by replacing the remote with a relay for confirmation.
If you think I'm wrong google: fog machine remote
In fact here is a good result, deals with making one remote work on a different brand of machines.
The timer versions work almost the same way, but have a circuit to press the switch for you at what ever interval (and duration) you have set on their dials.
Reheat frequency and duration are controlled in the machine, by how much heat (wattage) you can supply, and how much fluid is passing through.
Wireless versions just insert a RF link in place of the wires, so any connection (LOR relays) that work on a wired remote should work on a wireless fog machine too.
Machines will not respond unless the thermal switch in the machine has reached operating temp and enabled the demand switch (the wireless remote receiver).