Can fire spread to rooms that are connected via a ladder?
Thematically, I think it would make sense. However page 13 of the rulebook says:


  Investigators and humanoid (blue) monsters may move between spaces containing ladder markers as if they were adjacent. The spaces are considered adjacent for movement purposes only.


...which seems to suggest that doesn't apply to fire. As I commented on your question, I'd need to see the specific wording of the Pyromaniac card. Whilst I'd probably house rule it with my group to allow it, I suspect that you cannot if you're sticking strictly to the rules.