I happened to be playing with F9 blessed units w/ lots of attacks, so I ran a battle w/ logging -ddd. Here's the part of the log for a single attack in that battle. The attacking unit is a Prince General (MA Tien Chi sacred cav) ID 2547 wielding a Sword of Swiftness and a Stone Bird:
2547 striking with weapon
Sword of Swiftness. att28 def20
hitloc Prince General strikes Black Hunter wl2 diff2 -> 4
hitunit 2547 2029 dmg9 spec1 ba4
damage 5 on Black Hunter, spec0x1 ba4
hitloc Prince General strikes Black Hunter wl6 diff-2 -> 2
hitunit 2547 2029 dmg6 spec96 ba2
2547 striking with weapon
bless fire. att27 def16
hitloc Prince General strikes Black Hunter wl6 diff-2 -> 2
hitunit 2547 2029 dmg6 spec96 ba2
2547 striking with weapon
Lance. att28 def18
hitloc Prince General strikes Black Hunter wl4 diff0 -> 3
hitunit 2547 2029 dmg30 spec-2011168768 ba3
damage 17 on Black Hunter, spec0x88200000 ba3
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 1
hitunit 2547 2029 dmg6 spec96 ba1
damage 7 on Hunter Spider, spec0x60 ba1
2547 striking with weapon
Hoof. att25 def16
hitloc Prince General strikes Hunter Spider wl0 diff3 -> 4
hitunit 2547 2029 dmg10 spec136314880 ba4
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 2
hitunit 2547 2029 dmg6 spec96 ba2
damage 2 on Hunter Spider, spec0x60 ba2
2547 striking with weapon
Stone Bird. att40 def18
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 4
hitunit 2547 2029 dmg9 spec134217728 ba4
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 1
hitunit 2547 2029 dmg6 spec96 ba1
2547 striking with weapon
bless fire. att31 def15
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 1
hitunit 2547 2029 dmg6 spec96 ba1
damage 5 on Hunter Spider, spec0x60 ba1
2547 striking with weapon
bless fire. att27 def14
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 2
hitunit 2547 2029 dmg6 spec96 ba2
2547 striking with weapon
bless fire. att27 def18
hitloc Prince General strikes Hunter Spider wl6 diff-2 -> 1
hitunit 2547 2029 dmg6 spec96 ba1
As you see, the fire effect triggers for most attacks. I'm not sure why it doesn't trigger for the lance or hoof. OTOH, it seems to be triggering for 3 of the Stone Bird's 4 attacks.
I'm a little too busy to run more tests now, but maybe over the weekend... unless somebody else tests before then.