Technically, yes vapor from electronic cigarettes and vaporizers could set off the smoke detectors. This also depends on the type of fire alarm.
Heat detectors pose the fewest problems for vapors. They are the oldest and the least commonly used type of automatic fire detection device. Heat detectors feature a detecting element inside the unit that activates when it reaches a predetermined fixed temperature or when a specific increase in temperature has occurred.
An ionization smoke alarm contains a small amount of radioactive material. The radiation passes through an ionization chamber which is an air-filled space between two electrodes and permits a small, constant current between the electrodes. Any smoke that enters the chamber absorbs the alpha particles, which reduces the ionization and interrupts this current, setting off the alarm. With e-cigs producing vapor and not smoke which are different type of particles, they shouldn’t often set off ionization-based detectors, but they have been known to.
The most common and the most likely to be triggered by an e-cigarette are photoelectric detectors as they use optical light beams to detect smoke in their vicinity. If there’s enough smoke surrounding the detector, the light beam is broken, and the alarm is triggered. There’s less risk of this happening with vapor than there is with smoke, but it’s still possible.
The vapor from e-cigs does set off smoke detectors, but only when exhaling or blowing the vapor towards the smoke detector at close proximity. It’s not much different than smoking a cigarette in that regard. Vapor is less likely to set off a smoke alarm though, because unlike smoke, vapor dissipates much faster.