There are several fingerings for low Eb and they are all correct. It actually depends on what you are trying to play and the notes before and after the Eb. I use side Eb key most of the time - especially good for trills.
The auxillary key Eb I use only selectively, however other ways of playing Eb are 1st finger to the top (i.e. as if you're playing an E) with first finger on the bottom and 1st finger on the top with middle finger on the bottom. This is very useful technique and must be used if you're going from say B to Eb or Bb to Eb. It can also be applied to the upper register for Bb.
Sorry this sounds very confusing

- much easier with a fingering chart!
Basically there is no wrong or right, it is just which fingering is best for that particular bit of music.