by GamerAtom
Page 37:After a hero ends his movement (if any) during a move action of
the Quest Phase, his controlling player flips faceup any exploration
token in the hero’s area and resolves it.
the Quest Phase, his controlling player flips faceup any exploration
token in the hero’s area and resolves it.
I've bolded the part that specifies when they are revealed.
I believe the answer to your question is no. The Quest Phase occurs in Summer only and has nothing to do with the Mobilize or Conquest orders.
Scott can correct me if I'm wrong.