Yes and this why I'm second guessing the licensed electrician that I hired. The inspector told me they need to be on one lug.
So do I need to buy two 4/0 tri-plex?
No, no, no! You can't "just up-and decide to parallel". Since you are under NEC, paralleling requires a bunch of factors, including special equipment on the source side. Don't even dream of taking it on as an amateur, and the essential ingredient is a special cabinet rated for paralleling at the source.
Your best bet is to do it in one wire, so go up beyond 4/0 into the kcmil aka MCM wires, e.g. 1000 kcmil. And you definitely want to be in aluminum at that point.
I had to pay for 100' of 1000 kcmil copper to go 15 feet
. You don't want to do that lol.
(long story, Al wire would have been too big for the conduit, and since >1000kcmil Al is hard to find, it would've required triple-paralleling, and the special equipment we had was only equipped for 2 parallels. The special equipment included 6 fuses the size of a Magnum beer can.)
Service wires and feeder are required to be 83% of the rating of the service.
Only in NEC land. Power companies follow NESC. Totally different. Like French and German