The Summoner art is a lost art that recently got rediscovered so information on summoning is incomplete at best. Ysayle has a more knowledge of Summoning than Y'mhitra that's why she is able to summon Shiva by transforming into her. It does seem like npc characters have different knowledge of the Summoner arts than the pc so they can summon primals on a whim. Currently we are a baby Summoner just learning the art and in Heavensward we will hit puberty in the Summoning art and that's how we gain the power of the Elder Primal Bahamut.