I always assumed Hlaalu Helseth belongs with House Hlaalu but just to be sure, is there any concrete evidence showing that he is from Hlaalu or he isn't?

I had asked a similar question a long time ago myself. I always assumed he was apart of House Hlaalu. But the response was mixed. Some said he was, others said he wasn't.

His Great House is Hlaalu, which is why he's named Hlaalu Helseth (rather than Helseth Hlaalu). His minor house/family/clan is likely Llethan, just like his grand-uncle, the previous king.

Similarly, Nerevar's proper name was Lord Indoril Nerevar.

So for the Dunmer's royalty naming they follow Asian culture of putting family name first?

Not quite. It's not clear if Nerevar was a member of the Indoril family line or if that was the Great House he was aligned with. Helseth is also probably not of the actual Hlaalu bloodline. Instead, the ruler's name goes: Their Great House, their given name, their family name. Indoril Brindisi Dorom, a historical ruler Mournhold, could have his name expanded as Brindisi, of the Dorom family, and sworn to the Great House Indoril. The lack of a family name after Nerevar's given name may mean that he didn't know his parents, or that people who were born as commoners did not have family names at the time, or something else entirely. It's not clear if a certain level of authority is required to be able to prefix your Great House to your name, so it is possible that anyone may be able to style themselves in this manner.

Nerevar was actually Indoril Nerevar Mora according to an old dev post.

I think prefixing the great house name is just a formality issue, rather than something related to rank. We see it with nobles because that's who we're typically most formal with, but it's not exclusive to them. Plus, in most places, one's Great House should be obvious.

As i understand it, having the house name as a prefix means you're not of the house's founder's bloodline, suffix meaning you are. Hence the distinction between Voryn Dagoth* and Dagoth Gares for instance.

*Dagoth Ur being more of a moniker, i think. "Ur" means "proto-", "original", which fits with his whole style. He sees himself as the beginning of a new reality, after all.

That is why I said it follows Asian ways of naming. Family or Clan name first. Also before he was the King, he was called Helseth Hlaalu.

Not really no..again he is not of the Hlaalu bloodline but a member of the house.

And before he was king he was prince:

Before that he was

And there probably wasn't much need for Dunmer house names in Wayrest.

King Athyn Llethan was referred to normally with is house name last.