I don't advise punishment or ignoring. I think those things hurt the relationship. Mostly what works is prevention--keep them fed and not thirsty, pay attention to when they are getting frustrated so you can redirect before they get loud or start hitting, don't set them up for failure with long shopping trips or long restaurant meals.
But when it's really a tantrum, if you are home, you could let them have a minute to vent, get that adrenaline/cortisol out, then distract, sweep the kid up, get a snack, put on a tv show, let the dog out, etc. Change the mood with something new.
If you are out, pretty quickly get out of the way of others, if you can. I don't think it's ok to keep a screaming, flailing kid in a store or restaurant. I am not sure how you manage that with twins! Tricky.
I would make sure you always have lots of little, fun surprises in your bag--stickers, finger puppets, crayons, a balloon, little party toys, necklaces and bracelets, like silly bands--always have tricks to pull out to distract. Be creative. I've made stuff out of old receipts, made the plastic wipes container talk (use the lid like a mouth). Your capacity for silliness goes a long way at that age, be playful.
These days if I see my daughter starting to get riled up in public, I can sort of whisper close to her, "it's not ok to scream in here, the other people are eating, you'll bum them out, ok? want to play a game on my phone?" And she can help calm herself, get interested in something new, and we may stop something before it starts. But she's older.
At less than 2, she was more distractable, but less reasonable, if that makes sense--so it would work better to immediately offer something new and fun than to talk about it.
When everyone is calm, practice taking a big breath. Use blowing bubbles to practice, or balloons, or pinwheels. Over time, I've seen my daughter start to remember that breathing deep helps her. When she stubs a toe or something now, I see her consciously take a big breath. It took a long time before she would think of that in the moment though.
It's a good skill to practice, to be mindful, to focus on breathing when you don't feel calm, to slow down when you start to feel mad. Kids won't learn it all alone in time out, or by being ignored.