Did people at the turn of the previous century refer to the 1890's as "The Nineties" and so on with other decades?

Yes. Evelyn Waugh quite often refers to 'the Nineties' in his books when referring to the 1890s, especially in dialogue.

Also there's the film 'The Naughty Nineties' (which admittedly was made in 1945): http://en.wikipedia.org/wiki/The_Naughty_Nineties.