A topic from AEG's L5R CCG Rules forum, copied for Oracle of the Void from a copy of the forum saved in October 2015, so pages it didn't save are missing. Players' names are left out; the rules officials are named. Rulings are as they stood on these dates; later rulings, the rulebooks and the Rules Archive may differ.
Daikua
Keywords
Mantis Clan • Scout Text
Reaction: Before the Defender's first opportunity to take a Battle action or pass in the current battle, if you are not the Defender or if you are and the Attacker controls a Port or Naval card, bow Daikua and one of your Ports: Take an additional Battle action.
lets say i am the attacker and i have more naval guys than my opponent i declare a naval invasion, would i be able to use daikua's reaction right after i perform my first action as naval?
Daikua
Keywords
Mantis Clan • Scout Text
Reaction: Before the Defender's first opportunity to take a Battle action or pass in the current battle, if you are not the Defender or if you are and the Attacker controls a Port or Naval card, bow Daikua and one of your Ports: Take an additional Battle action.
lets say i am the attacker and i have more naval guys than my opponent i declare a naval invasion, would i be able to use daikua's reaction right after i perform my first action as naval?
Well, not "right after", but essentially yes.
You use the Naval Reaction "after engaging". When all Reactions "after engaging" have been taken, you get your Battle action from the opportunity granted to you by the Naval Reaction. Then, before the defender's first opportunity to take a Battle action, you may take Daikua's Reaction. You make take your additional action (or actions, if you use multiple Daikuas), then the Defender gets his first opportunity.