Radiant shield affects everyone in the party including other pets (lol selene and eos). I also believe that (based on logs) Ifrit does a counter attack whenever other targets get hit. It doesn't seem right that Ifrit is using radiant shield only when he is hit when in some fights he'll take literally no damage and still counter attack (take A3 for example).
http://www.fflogs.com/reports/7zZ4TR...-done&source=2
It goes without saying that no pet have an attack called "attack" (pet's don't auto attack, they use their base attack, in this case burning strike every 3 seconds). In the log I linked, Ifrit also used "attack" more times than burning strike, which leads to believe that he used attack for every physical hit received under the duration of radiant shield. Further digging through that log reveals that Ifrit took no damage during the encounter outside of splash and (aside from splash not being physical anyway) radiant shield was not active during the damage intake. Looking at the log though it seems that he will continue to use attack well past the duration of radiant shield.
Lots of controversial opinions here (particularly I'm challenging the opening post's opinion of Ifrit in post 58 content) so feel free to discuss any obvious oversights in the thought process, errors in the provided data, or contradictions in the logic.