I agree, subtext is something the author does throughout the work, in various ways. It is not necessarily a psychological leaning of their own, it can be an explicitly formulated principle. Nearly all books carry the subtext "Evil loses, good wins;" but that tends more to the 'psychological tendency' side of things, nearly all of us want good to triumph over evil.
But authors can go beyond that, to more closely define "good" and "evil" by the context of who gets punished and who does not. In many heroic stories, the subtext is clearly that violence per se is not a bad thing, because violence (even murder) can be done in the pursuit of defeating evil and the heroes will live happily ever after.
Likewise, a subtext of "gender equality works" can be presented, the author never has to say it, but can intentionally show it through the story. Or to be more explicit, "females can do everything males can do in battle (including triumph or die)".
Subtext can even cross multiple works: Many blacks have complained about the very biased frequency in Hollywood with which black characters are the first to die (a statistically valid observation rising well beyond plausible random chance, until recently), prompting a charge of a subtext for Hollywood writers and producers that blacks are more expendable than whites.
Women have complained about a similar dynamic in portraying females as having far fewer lines than males and seldom portrayed as anything like equals, more generally the object of pursuit or fantasy, or subordinate 'servants' to men.
Within a single work, subtext can serve as an excellent way to get across philosophical points the author wishes to express, without getting preachy and having some character make a long speech (that usually interrupts the story for the worse). Namely, the actions in violation of the subtext philosophy get punished, the action in keeping with it get rewarded, and the author engineers the story to show both types of outcome, repeatedly.
To answer "where to put it," the answer is nowhere, and everywhere. Subtext is not written [The 'nowhere' part of that prescription], it is the consequence of actions and drives the events and outcomes throughout the story [The 'everywhere' part of that prescription].