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.
A player, 30 April 2012
Can the Phoenix player draw a card if he destroys a card before battle resolution ?
Text Kami • Experienced • Unique After a battle resolution ends in which a Phoenix Clan player destroyed one or more provinces or enemy cards: He draws a card. Battle/Open: If you are a Phoenix Clan player, discard this card: Put a non-Unique Spell or Kiho in your discard pile into your hand.
Ben Higgins (rules official), 30 April 2012
Can the Phoenix player draw a card if he destroys a card before battle resolution ?
Text Kami • Experienced • Unique After a battle resolution ends in which a Phoenix Clan player destroyed one or more provinces or enemy cards: He draws a card. Battle/Open: If you are a Phoenix Clan player, discard this card: Put a non-Unique Spell or Kiho in your discard pile into your hand.
No.
The trigger for the trait is "After a battle resolution ends..."
This is a very specific point in time when resolving battles, found just after Step C, section 3 here.