The addition of the B.C. component happened two centuries after Dionysius, when the Venerable Bede of Northumbria published his "Ecclesiastical History of the English People" in 731, wrote Antonia Gransden, who was a reader in history at the University of Nottingham, in her book "Historical Writing in England: c. 500 to c. 1307" (Routledge, 1997). The work brought the A.D. system to the attention of more people and expanded it to include years before A.D. 1. Prior years were numbered to count backward to indicate the number of years an event had occurred "before Christ" or "B.C.
The B.C./A.D. system became more popular in the ninth century after Holy Roman Emperor Charlemagne adopted the system for dating acts of government throughout Europe."
https://www.livescience.com/45510-anno-domini.html
Before the adoption of this system dating was rather chaotic, with dates usually being recorded as "year X of the reign of so-and-so". To line dates up and synchronize them on a timeline was difficult, and synchronization of European, Islamic, Greek and Roman history wasn't even attempted until the 16th century (Scaliger's De Emendatione Temporum).
And then there's radiometric dating and dendrochronology, which are chaotic in their own right, but 300 years? Nah.
Weirdly, I was just reading Lynn White's Medieval technology and social change (1966), discussing the introduction of the stirrup and the heavy plow (as opposed to the scratch plow), both of which happened in this period. There's little in the way of good dates, but some very big changes such as the move from individual family subsistence farms to large, ridge-and-furrow strips and Charles Martel's redistribution of church lands to his followers, introducing true heavy cavalry and the feudal system. (Note: may be a bit out of date with modern research.)
Later historians simply took the official date for granted - so the people in Pope Gregory's time believed they were living in the year 1582, but, unbenknownst to them, only 1285 years had passed since the year 1CE. The real date was reflected in their astronomical calculations, leading to the 10 day correction instead of a 13-day one.
Of course, this is all absurd for all the reasons listed in the article, and others.