No that's not where they originated from.
> The idea that demographic trends are descrete or have some sort of constant period is ludicrous
Named generations don't have a constant period. (They tend to run between about 12 and 25 years.)
> I should point out that the "boomers" are real insofar that birthrates did rise and fall.
True.
> There's no "boomlet" caused by them.
Without attributing what caused it, there was a continuous nearly monotonic decline in US birthrates from the peak of the Baby Boom in 1954 through 1976 (Gen X is usually tagged as ending between 76 and 80, then a run up to a peak in 1990, followed by a drop back to the 1976 low in 1995, hovering around that point or slightly under through the end of the millennium, where it started dropping again.
The Millennial/Gen Y group does correspond to a boomlet.