Do you really think he flaunted his money and jewelry to everyone in Sedya Need or were they just jealous of him?

I suspect he had some wealth (being on the Imperial payroll), and that he may have had a bad attitude being stuck in a Vvardenfell swamp like Seyda Neen. Add to that the fact the tax man is never very popular and it's not very hard for me to see how that view of Processus was formed. Oh, there may have also been some jealousy because he was seeing the Dunmer lady at the light house.

Considering he's dressed in commoner's clothing and he only has the one ring given to him by his girlfriend in the lighthouse, I think it's more just "he's the damn taxman" at play.

Remember, the guy who murdered him had the largest of the unpaid taxes. He claimed that Vitelius was charging too much and skimming from the top. And stole the ring off the body; if Vitelius had other jewelry that Foryn stole (presumably to fence), why would Foryn still keep the one ring? And if that was the only thing Foryn stole, where's the rest of the jewelry?

Long story short, it's pretty much Foryn is lashing out against imperial rule and decided to take it out on Vitelius, likely because of the unpaid taxes issue. At least, according to all the evidence we have.

The apparent story is that Processus Vitelius wore the ring and "flaunted" it, which Foryn took as showing off his wealth, rather than his new girlfriend. It appears that Foryn assumed that if Processus had enough money for a nice ring like that, then either he was getting paid too much to collect taxes, or skimming off the tax payments. Simple solution in either case: kill the guy.

Only problem with that is that he recognizes the ring as likely having been given by the girlfriend if you tell him that you won't turn him in. Though he could have reconsidered after the event, he still sounds like he doesn't regret killing Processus.