I can see where this might be true, but I don't think we have enough information yet to say. Frixio doesn't flat out tell us that it was the summoning process itself that tempered the Slpyhs, only that all those that took part in it were eventually tempered, which would make sense because those Slyphs that summoned Ramuh would be on hand when he first arrived and so he could easily temper them himself.
I'm leery of using gameplay to figure out a lore timeline. The Sahagin dailies and the leviathan fight were both added in patch 2.2, which I think suggests that they would be happening side by side to each other in time, despite what order you actually do them in as a player.- Since this quest can be performed BEFORE you fight Leviathan in the Main Scenario (canonically, it has been many years since the last summoning), it's clear that the actual presence of the Primal is not required. (Unless they use a handful of crystals to summon an Egi or something.)