I've been told about this... Is that common knowledge in the West? It might be generally accepted among Japanese fans, at least the type of fans who care about this stuff.
How to read the tengu's newspaper numbers?
The facts:
Nearly all papers we see have very small numbers after the month, no larger than 5.
The only exception is Mystia's
article in BAiJR. It's numbered Year 120, 13th of October.
The speculation:
The months are months in the youkai's own lunar calendar system, which is widely used by the tengu (CoLA), not Gensokyo's Gregorian calendar.
Since the standard time unit in the youkai calendar is longer than a day (CoLA), the number following the month is not the day of the month.
Instead, it's most likely the number of issues in each month. "1st of February" means "the 1st issue of February".
It makes sense that Aya can make 4-5 issues of newspaper each month on her own.
The abnormal 13th issue is likely the result of a news competition, in which all tengu churn out many more papers than usual (CoLA).