Last year there were two competing songs expressing nostalgia for a clearly defined zeitgeist of the recent past -- "1999" by Charli XCX and "2002" by Anne-Marie. Both were the products of the current vulnerable, refractory phase of the 15-year cultural excitement cycle (2015-'19), when energy levels are drained after the last manic, invincible phase (2010-'14), before they will recover during the next warm-up phase (2020-'24). But one was referring back to a previous manic phase ('95-'99), and the other to a previous vulnerable phase (2000-'04). One did not match, the other did.
So far, the phase-matching song -- "2002" -- has been far more successful, and you still hear it being regularly played over a year later. Its creators and its audience are more able to resonate with it, since the zeitgeist of the song's setting matches their own, at least regarding the phase of the excitement cycle. Expecting people in a refractory period to resonate with a manic, high-energy zeitgeist -- "1999" -- may be asking too much of their physiology.
To investigate, I checked out Wikipedia's category list of nostalgia songs, which includes both of the above. I also looked through the Hot 100 year-end charts for titles with a year in them, in case the category list was missing some.
I'm interested in ones that are nostalgic for a narrowly defined cultural period -- one year, or less than five years at any rate. That eliminates songs that refer back to longer periods like several decades. And it eliminates those that are nostalgic for a certain stage of the lifespan, or for a previous romance, without any reference to what historical or cultural period it took place during.
I kept only those that resonated with audiences at all -- they had to make it onto some chart. Not necessarily the Hot 100, perhaps the rock or R&B charts, and just making it to the weekly charts (rather than year-end) was fine. Otherwise there aren't many to study.
Still, this leaves only 12 songs, which are listed below by their release date (album or single, whichever was first, not that it affected the phase it appeared in), which phase they were released in, the time they're set in, that setting's phase, and whether or not these phases matched. They are sorted by the phase of release date. Click for full-size.
As it turns out, there is no bias for nostalgic songs to be made during any of the three phases of the cycle -- each phase has produced 4 songs. There's no significant bias for the phase of the setting either -- 4 manic, 5 vulnerable, and 3 warm-up, barely distinguishable from the even distribution of 4, 4, 4.
However, there is a significant matching between the phase that the song was produced in and that it was set in. See footnote .
By the way, "December, 1963" originally came out during the late '70s warm-up phase, but it was remixed with a more modern dance sound, and charted once again during the early '90s warm-up phase. I left out that second recording, but including it would only strengthen the conclusion, adding another phase-matching song (since the early '60s were a warm-up phase).
So, rather than artists and audiences resonating with any old phase earlier in the excitement cycle, they are inclined to resonate with the same phase that they are currently experiencing.
To my ear the most resonant matches are "Summer of '69" for the manic phase, "December, 1963" for the warm-up phase, and "American Pie" for the vulnerable phase.
As for the mismatches, if only "1979" had been released a year earlier in 1994, that would have made it perfectly 15 years in sync with its setting. It doesn't really sound like a proper manic phase song of the late '90s anyway, but more of a "just getting the motor going" song typical of a warm-up phase.
All other things being equal, if you're going for nostalgia for a 1-to-5-year period, make it match in phase with the current phase of the excitement cycle.
 If the artists were choosing years to tell stories about without an inclination toward any of the three phases, then each phase would have an equal chance of being chosen, 1/3. So the chance of a match between the phases that the song is released in, and that the song is set in, would be 1/3. There are 12 independent songs. So the number of successful matches should be binomially distributed, with n = 12 and p = 1/3.
You'd naively expect 4 matches (12 * 1/3), and yet there are 8 matches.
The probability that there is a result so high above the expectation, or even higher, is less than 0.02.
We can therefore reject the initial assumption that the artists are just choosing years to tell stories about without an inclination toward any particular phase -- they are clearly inclined toward reminiscing about the same phase of the cycle as the one in which they're released.