Not only the vapor, but quitting smoking (or cutting down significantly) by any means triggers coughing; the body's attempt to get rid of the tar and crap in your lungs. I've quit smoking countless times over the years and ALWAYS coughed and hacked for a while. I about hacked up a lung or three when I started vaping!
Ditto the advice to drink LOTS of water...important to stay hydrated and vaping dries you out.
This, and all the other excellent comments as well. Do drink a lot of water!
When I quit smoking - and switched to vaping - I went to my doctor for other reasons after a couple of weeks. I told him I stopped cigarettes, though I was still vaping. He was ecstatic that I'd quit the tobacco cigarettes, and promptly started telling me what to expect over the next several months now that I'd stopped smoking. It included increased congestion, possibly for 5 to 10 months, as the cilia once destroyed by the smoke, tar, ash, and other chemicals from cigarette smoke now began to regrow and start pushing the mucus and other icky stuff up and away from the lungs up the "phlegm elevator." This, accompanied by allergies due to the season, was likely to make me pretty uncomfortable for a while, and he suggested using whatever over-the-counter decongestant worked for me - and would not interact with my other medications - until the symptoms begin to ease up. I only use the decongestant when I'm really miserable, and am controlling my own "recovery" from cigarette smoking. The doctor explained that eventually the coughing would turn into a "full" cough, meaning that what needs to be gotten rid of will be done so right away instead of the smokers' cough which keeps us constantly trying to hack up the gunk we inhaled after killing all our little cilia friends. In addition, our lungs start to slowly repair and regenerate tissue and slough off dead cells and contaminants for us to cough up, too. So, the congestion may actually seem worse even though we are in the process of healing.
And, welcome to ECF, Stocksdale!