I think the idea was that a fresh tub was soft and needed some time to cure making it more puncture resistant. This seemed to be the case with my Criteriums but I have no scientific reasoning to back it up.
I seem to remember doing same, both to stretch the tire and to "season" it, whatever that meant.
According to Eugene A Sloane, writing in the olden day, in the 1970s', in
The Complete Book of Bicycling, it was claimed that latex bonding with the tire casing hardened while the tubulars were being aged. You were to age them, on a rim, in a cool, dark place for six months. If you rode fresh tires, your tread may seperate from the casing, and you were more prone to flats. This is a paraphrase of page 394. Spoiled milk was also used as a preventative against small punctures.