The unchained summoner has the spell-like ability to cast a summon spell, with increasing strength as they level up.
Starting at 1st level, a summoner can cast summon monster I as a spell-like ability a number of times per day equal to 3 + his Charisma modifier. Drawing upon this ability uses up the same power as the summoner uses to call his eidolon. As a result, he can only use this ability when his eidolon is not summoned. He can cast this spell as a standard action and the creatures remain for 1 minute per level (instead of 1 round per level). At 3rd level, and every 2 levels thereafter, the power of this ability increases by one spell level, allowing him to summon more powerful creatures (to a maximum of summon monster IX at 17th level). At 19th level, this ability can be used as gate or summon monster IX. If used as gate, the summoner must pay any required material components. A summoner cannot have more than one summon monster or gate spell active in this way at one time. If this ability is used again, any existing summon monster or gate immediately ends. These summon spells are considered to be part of his spell list for the purposes of spell trigger and spell completion items. In addition, he can expend uses of this ability to fufill the construction requirements of any magic item he creates, so long as he can use this ability to cast the required spell.
Augment Summoning is given as a bonus feat to the master summoner, so certainly that's intended to work. The SLA acts as a spell, but is it actually a summon spell?
Each creature you conjure with any summon spell gains a +4 enhancement bonus to Strength and Constitution for the duration of the spell that summoned it.
Versatile Summon Monster says it works with an effect that mimics such a spell, so clearly it works.
Evolved Summoned Monster says Each time you cast a summon monster spell, and you're not casting a spell, so it shouldn't work.
Superior Summoning says Each time you cast a summoning spell, and you're not casting a spell, so it shouldn't work.
As a counterpoint, the Leanan Sidhe has Spell Focus (enchantment), which applies to its SLAs.