The 20 W has it, and I presume that all the iSticks have it also: a brief lag between the tap on the firing button and the actual current being provided to the atomizer. That's because of two main things. Firstly, the device is always checking the atomizer resistance, with a 100 mV current in the 20W. I don't remember how often it does it, but it is surely less than one second between pulses. That's how it reads the resistance in real-time (at least meanwhile the screen is on). Busardo's depiction of it in its review of the 20W was 'it has a heart-beat, I'm not sure why, but it has it...'
But they also have to discern between taps for firing and taps for setting things up, like changing the VV/VW mode (three clicks) or powering the device itself on/off (5x). eLeaf's designers decided not to feed the atomizer in those taps.
I wonder if that delay could be misinterpreted as a soft firing after all, when you are driving the 50W at high settings......