I had 2 deploys in hand, both had full mana, cast the first card with fires of invention in play and summoned 3 creatures. The second deploy is then disabled due to fires of invention.
Fires of invention states 2 cards are cast before the rest are disabled, however, only 1 card in this situation was cast from hand, and yet FoI blocks any new cards from being played.
Even though Deploy drops 3 critters on the battlefield, these creatures are not cast from hand and therefore should not count against the 2 cast card limit of FoI.
When reviewing the battle log, the creatures played from Deploy are listed as cast, which may be part of the problem.