Vulcain was not the first to launch a wrist alarm. Eterna patented one by 1914 (and officially aunched at the Swiss National Exhibition in Berne that same year), which can be considered the first commercial wrist alarm produced.
(here it is) (nice enamel dial BTW...)
Now, it is common knowledge that Jaeger LeCoultre, when they saw the early success of the Vulcain Cricket (first mass-produced wrist-alarm), asked to its watchmakers team to copy it to occupy this new small-complication segment (the design and specifications brief specifically referred to the Vulcain Cricket).
So, the initial hand-wound memovox was actually a mee-too of the Cricket (slightly less effective as you could not really engage / disengage the alarm like was patented in the vulcain brevet with the use of a button).
Jaeger LeCoultre indeed later improved the alarm wristwatch by combining it with an automatic-winding system for the time barrel (a clever re-engineering of the bumper rotor principle to allow for a case-back alarm stem).
Omega (/ lemania) later took the technological lead by adding an automatic winding system for both time and alarm functionalities (rotor was winding both time and alarm barrels, one in each direction), and an accurate-to-the minute setting of the alarm time (using two center disk indicators), and, like for the Vulcain, the ability to start / stop the alarm feature at the push of a button.
The Omega Memomatic alarm wristwatch system is unsurpassed to this day (except in much higher-end special timepieces à la Breguet Reveil du Tsar), and it is a pitty that Omega doesn't offer a modern Memomatic in its current line-up.