Assuming Summoner is going to be a pet job, I would want it to be built on a less restrictive foundation. Then we can worry about avatars and whatnot. My suggestion would be:

Class: Evoker
Weapon: Crystal Orb, Tamagushi

(note: these are random levels selected)
1. Call
1. Attack - Summoned entity attacks target enemy.
5. Astral Burst - The avatar uses a concentrated magic attack.
7. Symbiosis - Sacrifice some HP to restore 2.5 times the amount to your avatar.
10. Astral Assault - The avatar uses an attack ability
17. Borrowed Burst - You borrow power from your avatar, releasing a magic attack of the same elemental alignment as your summoned avatar
20. Astral Ward - Your avatar uses a defensive or support-oriented ability
...and so on

The basic idea in this case is that the summoner's "abilities" have general names, but the actions themselves are specific for the avatar summoned. Say the SMN has Carbuncle out and they use Astral Ward. Carbuncle would use Wall (FFVII version) on the party. If the SMN had Diabolos out and used Astral Ward, then Diabolos would use Punishing Barbs. If it's Phoenix then Blaze Spikes, and so on.

Likewise, if the SMN uses Borrowed Power while Diabolos is out, the SMN therefore casts Demi. If it's Phoenix then the SMN casts Fire.

Astral Burst would be unique abilities that are native to the avatars but not on the same level as Astral Flow. Like Phoenix's Astral Burst could be Firebird, an AoE attack that does damage to the enemies and does 10% of the damage dealt to Phoenix, as opposed to its Astral Flow, Flames of Rebirth, which deals big damage and heals the party for a portion of the damage dealt.

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Another option would be the Evoker/SMN having only call and auto attack abilities, and the rest of their action bar being determined by the Avatar that's out. This would help assign roles to specific avatars (healing on carbucle, tanking on Golem, damage on Ixion, damage + heals on Phoenix).

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For both ideas, what I'm aiming for is the Summoner gaining abilities of their own from the Avatar, aside from having the Avatar's contributions to combat.