Hi Wevian,
I'm sorry if I'm interpreting this incorrectly, but that large peak is the result of an equilibration without a column? Sorry, I'm a little confused with your wording. You couldn't have placed a column on in the middle of an equilibration, correct?
By any chance, does this peak increase with longer equilibration times? I would test and see if that is the case, if so then there is definitely some contamination occurring somewhere in your LC. It seems like it is not the result of the column (if I'm interpreting what you said correctly), which could have down-stream effects like the drift you're seeing. Mayhaps your strictly-water MP bottle has some contamination in it that builds up, and then when you put your actual mobile-phase on (azide,PBS), the contamination mostly elutes (the large peak), followed by some of it slowly eluting from the source/farther up from the primary spot of contamination (ie, tubes right at the MP reservoir following your wash with water)? The peak comes out pretty late, so there seems to be a decent amount of retention (if there is in-fact a column in-line for the picture you posted). Keep the column on, try equilibrating for a longer period, and then update us following your next wash with your proper mobile phase (azide,PBS). If there is an increase in area/size, then it's safe to assume you have some contamination up-stream from the column that may be introduced through the water your are eq-ing in.
Have you attempted to switch mobile phases and bottles to different sources? I'd also try this to see if the drifting shortens or disappears. Depending on the location of this contamination however, it could be in one of your sinker frits and potentially infect other bottles, but we should know if that's the case following those few tests.
Best of luck,
Tyler Smith.