Should I insulate between 2 PCB's when SMT joining them together?
In general, solder mask should not be relied upon as insulation. So it's a bad construction even if it's not the source of your problem. A thin (maybe 0.1mm including adhesive) layer of Kapton (polyimide) tape would eliminate any possibility of shorting and would not affect it mechanically much. Your assembly house can also get die-cut Kapton stickers in various sizes. I would request this construction in any case.
Eg.  (source as per watermark)
I doubt you smelled ozone unless you have a kV source hidden somewhere, maybe burning insulation.
It's also quite possible (maybe likely) that you are doing something to the module to cause it to latch up and the resulting high currents are causing your exciting side effects. Typical causes of that include forcing inputs high when power is not applied to the circuitry and test probes slipping.
If you add some moderate amount of resistance such as 100 ohms on signal lines between the main board and module you can prevent much of that potential issue. Or just make sure that the main board can never be hot plugged or powered without powering the module.