Nope, that's it. Belias' mention is based entirely on the Summoner job crystals Tristan has stolen. Soul crystals are passed from owner to owner, carrying with them some degree of influence over the successor's acquisition of skills, seemingly somewhat dependent on their sensitivity - essentially, they're materia for jobs. In the Summoner storyline, Tristan makes a deal with an Ascian underling for the power to avenge his brother, slain by Ifrit (this is why Tristain carries Ifrit's Grimoire instead of a relic, like most other jobs' main characters; one, the Veil seems to be one-of-a-kind, and two, it shows that Tristan has defeated Ifrit and is eligible to be a summoner).

In exchange for the accumulation of Summoner job crystals (at any cost), the Ascian agreed to awaken the knowledge and power from within them and transfer it to Tristan. When he does so, part of the knowledge transferred is the memory of a long-forgotten primal faced by the Allagan SMN who once held the stone: Belias. This "awakens the primal's slumbering essence," and allows Tristan to summon its essence. That's why the primal is referred to as an elder, its essence has been around for a long time.

Why the Ascian wanted Allagan SMN stones?
Who originally worshiped Belias?
Why Belias looks like a big purple Ifrit?

All up for grabs.