Is it normal for joist hangers to be hung upside down like this?

Your contractor is right, and this is actually a known detail. When the joists sit on top of the beams out past the house, the rim board isn't holding anything up. It's the opposite: the rim board is hanging off the ends of the joists, and all the actual load is going down through the joists into the beams. In that setup the hangers aren't there to carry the joists, they're there to stop the rim from sliding down or dropping away. So the flanges end up bearing up under the rim instead of on top of the joists, which is why they look flipped to you. I've done it this way on my own build after scratching my head at the same thing, and it made sense once it was explained.

Your instinct about shrinkage is reasonable but it cuts the other way here. As the joist tails shrink and move over the years, that rim wants to drop with them. The upside down hangers tie the rim back up to the joists so it can't creep down or pull loose. Nails into end grain alone would be the weaker option in this configuration, which is exactly the problem those hangers solve. As for the ledger question, yes, absolutely ask to see it before anything gets closed in. You want to confirm the joists land on the ledger or on hangers at the house, or that there's proper bearing somewhere if there's a break. Once decking and fascia go on, verifying that means tearing work back out, and nobody wants that conversation. A ten minute look now, photos for your records, and you're covered. It's a completely normal thing to ask for, any decent builder will walk you through it without getting defensive.

Glad someone explained this because I stared at the same thing on my brother's build two summers ago and nearly made a fool of myself telling him his hangers were on wrong. One thing I'd add is to check what fasteners went into those flipped hangers, since they still need the right nails in every hole to do thier job holding the rim up, and it's an easy spot for a crew to get lazy on a detail they consider minor. Also second the photos, I have a folder from my own deck with a shot of every connection before the boards went down and it has settled more than one argument since.

Same deal on my rebuild last spring, flipped hangers and all, and my inspector didn't even blink at them. What he did poke at was the beam bearing out at the posts, so while you've got things open, eyeball that too. Make sure the beam is sitting full on the post caps and not hanging off the edge or shimmed up. On mine I measured and the middle post was about a half inch off center, easy fix while everythign was exposed. Once the fascia and skirt boards go on you can't see any of that stuff, so a five minute look now beats regrets later.