Nowadays we refer to decades in the 1900s at the '20s, '70s, '90s, etc. During the 1900s were these expressions used to describe the 1800s and simply jumped a century naturally as the 1900s went on, or is these kinds of references modern sayings.
From my experience with memoirs and autobiographies of people having lived in the second half of the 1800s and writing and publishing their works in the first half of the 1900s, they would definitely refer to the decades of the 1800s as the '70s, '80s, '90s.
But as you say, when the 1900s went on one would increasingly need to specifically mention the century as well, since tradition of referring to decades only would be transferred to the 1900s decades.
Curiously I have not encountered a widespread usage of referring to decades in that way from people living in the 18th century (my main field), it seems to be something that only became common in the second half of the 19th century.