either the atomizer is getting 3.7V or no volts. It would give you the top hat read out on an oscilloscope that any digital device should give: +5V or 0V.
Nope! No regulator there. The atomizer is getting probably 3.3~4.2v. Which is decidedly analog - you're not going to see any pretty top-hat if you're reading the voltage at the anode. The longer you draw, the lower the voltage and higher the current as the device heats and its internal resistance drops. Otherwise a 13 second draw would be the same temp as a 1 second draw. We can also observe this as we stop drawing and the LED dims to its zero state and the atomizer slowly percolates down.
I haven't measured the battery or pulled a part number off of it, but I'd guess it's probably a 2C LiIon, and typically, given internal resistance, probably 4.2v at full charge on the surface. I'll pull a single cell LiIon down to 3.1 in a deep cycle environment, 3.2 if I'm not feeling like taking the risk. 3.3 is pretty typical in consumer applications.
Fwiw I'm an electrician with 6 years of schooling. Or at least used to be till the economy turned me back into a pizza delivery driver.
Also FWIW: BSc/Physics, MS/EE [emphasis on CS and Firmware Engr'ing in embedded systems], MS/Math [emphasis on applied mathematics]
Normally I'd be obnoxious and disassemble one, toss it on the storage scope, capture the run, and post it - but alas, my lab is in boxes as I'm moving. [pout]