This is what is called a "kettle sour", because you're souring it in your boil kettle, then reboiling. This gives pretty precise control over how much you sour it. This IMO, is the main reason for the specifics on the starter. You're leaving it in there for a short period of time, and you need a good yeast count for it to get the job done. The author of the recipe may have planned the yeast count vs. the time left in the kettle. 18-36 hours actually seems a bit excessive. Some pro brewers might just do theirs overnight and they determine when it is done based on pH level.
You don't need a stir plate to make a starter... while a stir plate is more
efficient, using a growler is just fine. No need to over complicate it. There are calculators out there which will tell you expected cell count production in a starter with or without a stir plate.
I would wager he tells you to get the starter warm(er) because the primary goal is to get the starter/yeast to match the temp of the boil kettle (which is still quite warm). A major immediate temperature shift in a yeast slurry can blow the cell walls and kill the yeast. They can survive in a wide range, but an instant 40* rise is tough on the bugs.
If this was going to be soured and aged in the fermenter... I might suggest that the starter isn't required, as it'll have plenty of time to do it's work, but there is such a low yeast count in a liquid yeast vial that a starter is almost always a must; that said, sours, eh, I dunno, they're a different ball game. I'm trying to master this myself.