To be far there's a difference between a meltdown and a tantrum. A tantrum is something a kid chooses to because they didn't get their way. A meltdown is something a lot less voluntary and is more like a computer overheating after trying to run too much shit for too long. Of course both aren't really tolerated in public, though.
When I worked at Kroger (which is a terrible idea for someone on the spectrum BTW) trying to fend off meltdowns was a daily, shitty experience. If it got particilarily bad I'd sneak off to the restroom and self injure, which actually broke a couple years being clean (something I haven't accomplished since, sadly).
Best way to deal with meltdowns IMHO is to try and hole away in a quiet, non crowded place for a bit or try to limit time spent in over stimulating places (like try not to spend more than 30 minutes at the grocery store, avoid a coffee shop that has a loud grinder, etc).
Wow I just realized I hijacked this thread to blab about the sperg life for the past couple pages.