I have been involved in winemaking in all capacities from stripping grapes from the bunches as a child of 8 in 1950 to making my own wine from grapes, then juice and finally kits. We did not differentiate a "primary" and "secondary" fermentation, it was all just fermentation. This started in an open barrel and lasted from 10 to 14 days. Wine was removed from the fermenting barrels via a plug near the bottom of the upright barrel and moved to barrels supported on their side with the bung hole open. First run wine was segregated and marked, "Per La Famiglia." Occasionally, a "second wine" was made by not pressing the grapes at all, just capturing the free run and then adding water and sugar to the unpressed grapes (I don't recall the amounts as this was my grandfather's method) to restart fermentation.
The wine would continue to ferment closed ended barrels, with the CO2 escaping through the open bung and the level in the barrel was filled more than once a day as wine was absorbed by the barrel or evaporated. The process usually began during the second week of October (when wine grapes from California were available in Pittsburgh) and the barrel was sealed with a bung early in December. The wine would be drinkable at Easter, and it would improve with age. Early on we had no carboys or demijohns (although they came later), no yeast was ever added nor were any other additions made. Then, sometime in the 1960's a minor miracle occurred with the availability of Sodium Metabisulfite. We had to send to somewhere in New York for the chemical and the cost was outrageous, about $5 for a tube which may have contained 2 or 3 tablespoons full.
The wine was a very good table wine from 75% Zinfandel grapes and 25% Muscat grapes, co-fermented. On at least one occasion we used Alicante grapes in place of Zinfandel (can't recall the reason why but likely because my grandfather thought they tasted better). I should also mention that the fermenting barrels were 53-gallon, former whisky barrels from Schenley Distillery outside of Pittsburgh which we purchased for $5 each, and they probably had $5 worth of whiskey still in them!