According to the this post...
Essentially, the defeating of the Primals may be more of a standalone gameplay element used to pad out the length of the Job's questline, rather than one supported by Lore.
Quote:Summoners (the job)
- Primal Slayers?
Not exactly. Summoners need only to perform a ritual to summon a Primals' egi, and then defeat that egi to bind it to them (yep, all they have to defeat is that mini Ifrit, Garuda or Titan you see floating behind them). It's made very clear that in the lore, the actual Primals themselves are not summoned and do not need to be defeated to obtain their egi.
- Origins
Summoners as we know them today actually practice arcane arts developed by Allagan mages. The term "egi" is an Allagan word meaning "pure" or the "essence of", so for example "Ifrit-egi" literally translates as "the essence of Ifrit". Allagan summoners basically found a way to siphon the essence of Primals and manifest this essence as an egi, which is bound to do their bidding.
Essentially, the defeating of the Primals may be more of a standalone gameplay element used to pad out the length of the Job's questline, rather than one supported by Lore.