yes, you are right in assuming he means 1899 - 1900-ish, often lso known as 'fin de siecle' - why use plain english when you can alienate the servants with foreign talk :)
I think you raise an important point though: westernised global society only appears to have reflected extensively on its 'recent' past in the 20th century, so in 1990 everyone was familiar with 'turn of the centiury' meaning 1899 - 1900. With the turn of a new century, the water is muddied. Turn of the century now quite validly means 1999 - 2000 ish.
People writing about more distant times would be careful to place the reader in a clear context before throwing in a phrase of this type.
But with Miller he's clearly alluding to the general nuttiness, drug-taking and arty set around in 'decadent' Vienna which included Schiele and Klimt and his barenakedladypaintings and psychedilic textures.