I'm afraid I don't know the precise biology of this either but I have always assumed, dangerous though that may be, that it is the build up of biofilm and heterotrophic bacteria in older tanks that makes the difference. New tanks have very little biofilm, and shrimp and Otos, among others, feed on this heavily. So there has to be a decent layer of it on most, if not all, of the surfaces, to support them.
Plants seem to play a role too. Planted tanks seem to mature faster, at least, those I've had that are planted appear to have more biofilm sooner than tanks lacking plants. Using rocks or wood from an established tank seems to help some too.. perhaps not unlike seeding a filter.
Shrimp, Oto cats and many loaches are just a few of the species said to do best in mature tanks. I have found, through my efforts at raising Ghost shrimp, that adding green water to a tank helps establish biofilm much faster than it otherwise would build up. Not at all sure why that happens but it does happen. This is along the line of adding about 100 CC of cultured green water to a 5G tank twice a day for a few weeks, while the shrimp are larvae and for awhile after they morph.. about 3 weeks altogether.
By the end of the 3 weeks, the tank was supporting baby shrimp without my having to feed them anything at all, though of course I did feed them.. but only once a week. A few microworms, a fragment of algae pellet or tab, once a week or so.
For now, that's all I know, but experience with my tanks over the past couple of years seems to support the biofilm as being at least a large part of this.. if not the whole of it.
I think 4 months would be the minimum, and 6 months is better, if you aren't adding green water or used rocks or plants to a tank.