What does Cellular Automata Pre-image problem actually means?
The way I understand it, the answer is your item #2.

That is, the specific CA is fixed (i.e., rule 90 or rule 110, or what ever), and given that fixed CA, one gives you a (sub)configuration, and asks whether there exists another configuration that leads to the input (sub)configuration within $K$ steps. 

Indeed the description there (in the introduction of the paper) is very informal, but this is only because the 
the problem is formally stated in section 3:


  CAP (CA Preimage problem):
  Given: A fixed CA $(Q,\delta)$ and a configuration substring $s$.
  Question: Is there a configuration substring $s_0$ such that $s_0 \vdash^{K} s$, where $K= |s|$?