Melee Timid Pets' Imaginary Attacks

I don't know if there's data about this but thanks to my boredom farming Eerie, I found out that melee timid pets' imaginary attacks HAVE proration (I used red steel slayer, only me and the pet is in the PT) and aggro (which applies also to Gentle Pets; while taming, my gentle pet which has only MP gain... no buff... steals the aggro everytime I stare and let the mob attack me), though it doesn't seem to have ampr. On the other hand, there are pets that are unable to set their normal attack patterns which may not have proration (like the new bonefish tamable pet).

Significance? For me, I had an idea to have staff/timid pet which spams heavy magic skills using imaginary attacks' proration, relying on timid's special MP regen and skill MP gain, so it'll still be useful and prorate with itself even in a party of at most three persons. I don't know why, but my melee timid "bonefish" pet keeps spamming Blinding Shadow (2MP) like a gentle pet spamming Resistance Up (also 2MP).

The cut from the start of the pic is exactly the start of first battle, the second one is I waited for my pet's MP be depleted and made sure it's like "staring" at the enemy (the pet I called here has no attack skills, OHS/Genius/Timid Sand Bandits Potum w/ 200% normal attack pattern).
If the boss def/resist changes depending on time, then this is inaccurate or false.