There doesn't seem to be any difference between Eikons and Primals, after all; Eikon is just the Allagan term for them, much like Primal is the current term for them (except for Garleans).

It was only after the original Bahamut was defeated by the Allagans did the people of Meracydia took to summoning them. It was noted that no evidence existed of summoning took place prior to his defeat and was speculated that a 3rd party was involved teaching them the method... so Asciens most likely.

Many Eikons were summoned, it's just that the Triad were the most powerful of the bunch. They also warred against each other as well.

Bahamut was known a the "dawn wyrm", while Tiamat was "dusk wyrm"