Size of intersection of two acyclic DFAs A and B is O(|A|+|B|)?
Lemma 4 and Lemma 8 in your paper show that even for a fixed size alphabet, there are infinitely many finite languages with minimal DFAs $A,B$ of sizes tending to infinity such that the minimal DFAs for the intersection and union languages has $\Omega(\min(|A|,|B|)^2)$ states.