Adding new joists to old deck: lumber size mismatch

Edit 2: Turns out that this product is PVC plastic, and uses a HIDfast hidden fastening system Fastener System, Azek decking product installation videos. The product is also tongue and groove. Sounds like the contractor did a good job.

I would not build a deck that way for a couple of reasons.

First, decks should have some space between the boards for drainage. Otherwise water pools, accelerates rotting of the wood and makes the deck slippery.

Second is expansion. Given that outdoor boards are alternately soaked and baked, there is significant shrinking and expanding of the boards (another reason for gaps). That will be most pronounced in the width of the board versus the thickness. As the board expands it pulls out the nail. If the nail is pounded into the edge it will pull out more since there is more expansion in that direction compared to a vertical nail.

Screws don't pull out at all, and that's their principle advantage and why I always screw down deckboards. Nails are preferred by many, but I haven't seen them nailed into the edge, and I think it's for good reason.

Edit: if it's a composite as others have suggested, everything I just wrote is a waste of pixels. Unread it.

Around here, 4x4s are not uncommon. This table shows that a 4x4 pine post that is 6 ft or shorter can support a load area of up to 10 ft² assuming 50 lbs/ft².

Don't trust me or a random table on the internet; make our own calculations from tables in the building code or other trusted sources and consider having them checked by an engineer.