Platform:
Any

ISP:
Bredbandsbolaget

Type of Internet Connection:
Cable

Internet Connection Speed:
100Mbit/s

Date & Time:
Any time

Frequency:
Always

Character Name:
Mellowy

Race:
Mithra

World:
Phoenix

Main Job:
Summoner (I believe Beastmaster and Puppetmaster could also have this problem)

Support Job:
White mage

Area and Coordinates:
Abyssea zones

Party or Solo:
Any

NPC Name:
None

Monster Name:
None

Steps:
1. Get Cruor Buffs
2. Watch your own HP (It will be large)
3. Send pet on a monster and notice how much HP it has (It will be same as before)

I've noticed this best when I have 2000 HP on my Summoner, and my avatars die from 1500 damage. I'm quite sure the pets have at least as much HP as my Summoner without cruor bonuses, and should have simillar after cruor bonuses.

Another case could be that key items boosting cruor buffs do not work on pets. (Then I'd get something like 10% HP on pet, and 50% HP on myself).

Since Atma work on pets, it just seems reasonable that cruor bonuses would as well.