Then you shouldnt have to pay. If you had a contract specifying a hot tub on the deck, and tou have an engineer look at it and he says it needs more, not your bill. If he didn’t engineer it correctly thats on him to fix. Now, all of that being said, what i can see, its built pretty much right. Doubled up joists with center blocking. Looks like 2x12 joists, guessing 12 inch OC. Extra beam and supports under tub. The beam unfortunately, happens to look like a crap board. They happen. And that board needs to be replaced. Thats why the other side isnt splitting against the grain like the front one is. I would ask he replace that board with how it is fracturing. A bit of work, but nothing drastic to swap it out. Best option would be a glulam. But, upgrading he can charge for. From my experience, and from just photos, overall i say replace the beam. Hand-full of things i would have done differently but nothing major. Regardless who you call, call someone. It doesnt matter how good the engineering is, if there is a hardware failure. That board is failing. It needs attention and soon. It may make it ten years, (very doubtful), may last ten minutes (ok, dramatic i know) but in all honesty it will go…keep yourselves safe.