[He was still wrapping is head around who would put them in a vending machine?, but at least them being inside the pokeballs would offer them some protection—]

Yes, Tepig is a fire type from a region known as Unova usually given as one of three starter choices.

[There was a tap to his jacket pocket, and out came floating his rotom phone, scrolling through to an app.

He did reach to pet the little kitten of a pokémon on Houndoom's head of course.]

You are correct. This little one is a Litten, another fire type from Alola. Again usually given as one of three choices for a new trainer's first pokémon.

[He was detecting a pattern.]