To be honest, the base of summoner is fine, there are just tweaks to the details I would want to make so it's an actual pet class not a DoT class who happens to have a pet. And some changes to the pets dynamic so you don't just use one pet. And obviously aesthetically I want them bigger as I've said in many other threads on the topic.
First: (now don't pounce until you read the whole thing) take contagion -and carbuncle's version- off of Garuda and emerald carbuncle. These moves combined with the fact that SMN is so primarily focused on its DoT's make them the egi of choice and that's bad. Now I'm not saying remove it from the job completely, it's a good skill, in fact it's a great skill for the job. What I want is to swap it with tri-disaster. So the summoner is the one using contagion, not the pet. This would do 2 things to improve the state of SMN, it would free up the SMN to pick whichever summon is best, rather than just Garuda full time. Second it would allow the summoner to extend their own DoT duration giving them the chance to focus entirely on their pet rather than worry about if their DoT's are still up.
Second: rework the egi dynamics, now I said swap contagion with tri-disaster, but it's not just a swap, I want to rework how Garuda and emerald carbuncle relate. I want Carbuncle to fulfil a minor crowd control role, backdraft for knockback, something to silence, something to bind. Now when changing to Garuda, instead of getting a damage increase, all those skills should become AoE. This would make ifrit better for single targets due to his higher damage, I.E bosses, while Garuda would be more suited to trash mobs for her crowd control element. Titan is fine as the solo pet for tanking.
Third: remove fester, (again don't pounce) fester is a great skill but it's a skill that takes away from the pet class element and puts it on the SMN themself. What I want is to replace it with a move that works like a weaker version of enkindle. When used it will order the pet to use a move that will vary based on which pet uses it.
Garuda, feather rain. AoE with light damage that inflicts heavy on all mobs inflicted with the masters DoT's (think of it like the feathers being attracted to the DoT's to explode). The degree of heavy will vary based on the number of DoT's I.E 1 DoT 5% heavy, 2 10% heavy etc.
Ifrit would do incinerate, a frontal cone attack where the damage increases based on the number of DoT's, essentially the current fester but frontal cone and on ifrit instead of the SMN.
Titan would do tumult, AoE around Titan, increase enmity, number of hits varies with how many DoT's are on titan's current target.
This move would have same recast as fester and require atherflow charges to use it. It would really just place the focus of SMN on the pet rather than the SMN themself, aswell as increase their AoE utility a bit.
Fourth: Enkindle, recast reduction. Not much, 3 mins recast maybe? Just seems more reasonable.
Final note: Only other thing I can think of would be increase spur potency, it is kind of lackluster, just make it have more potency than rouse, it seems only fair with it not getting all the other goodies rouse gives and with my changes SMN pet is the main focus so it deserves a few seconds of super power. Or perhaps a full heal on the pet instead of making it stronger than rouse, sometimes when your pet is getting beaten down, or even just being an idiot and standing in DoT circles, sustain and SMN physick isn't always enough to save it in time. Adding a full heal to spur might remedy that a bit.
Oh and change radiant shield on ifrit to crimson howl (enfire) seeing as he should not be getting hit and in a situation where he is you should probably be using Titan anyway.