I keep seeing builds of the Monster Tactitian recommend taking the Spell Focus (conjuration) and Augment Summoning feats, but does that actually affect your summons or does it just seem like it should? Those feats only affect spells, while your summon monster ability is a spell-like ability. In the tabletop version of the game, I know there is some argument over where this distinction matters and where it doesn’t, so before I build my PC and waste my first two feats can anyone tell me for sure that it 100% works on your summons?

No idea if it affects an MT's summons, but even if it did it would not really be worth 2 entire feats.
Only a druid could get enough out of it to justify 2 feats imho.

If going for a MT i can reccomend the nature path for an animal companion (basically get 2 subclasses in 1), and also adding 1lv rogue and 1lv vivisectionist + accomplished sneak attack.
Should avoid the mastadon pet tho, as he is simply too large (aswell as annoyingly loud) and gets in the way more than anything.

I did a small test. I created 2 human characters that are the same with the exception that one has the spell focus and augmented summoning and the other one has some random feats that dont affect summoned creatures. Then I summoned a dog in the prologue and let him attack some enemies. With the feat, the dog had +3 strength bonus to attack roll. Without it the dog had only +1 strength bonus to attack rolls. Based on that my conclusion is that the feats works with monster tactician summons.
Human characters are nice for testing feats in prologue like that :)