"Webby's a terrific guy," Tevaga told the Herald. "I had him early in my career and I've experienced his coaching in the Toa Samoa camp. He likes to enjoy himself but you work hard first and then you get to enjoy yourself.
"I've already had a conversation with him. We are going to have a lot of fun, but we are also going to put in a lot of hard work. I can't wait."
While Tevaga endorses the Webster appointment, he retains a lot of loyalty towards interim boss Stacey Jones, having first played under him almost a decade ago.
"He has been my coach coming right through the grades and I would've loved Stacey to take the role," said Tevaga. "But that is not something he wants to do so I'm backing Webby as well.
"We'll enjoy the rest of the season under Stacey and when Webby comes we will put in a lot of hard work for sure."
The 26-year-old managed a typically wholehearted effort in Friday's 28-18 defeat to Parramatta.
Restricted to 51 minutes, after battling a virus, he accrued 101 metres from 11 runs, along with 39 tackles.
"I was rooted," said Tevaga. "My lungs were stuffed. I was coughing up a storm."
Tevaga was one of several players, along with Josh Curran, Freddie Lussick and Reece Walsh, who were underpowered coming into the game, after recent illness.
"During bye week, that was probably the sickest I have ever been," said Tevaga. "That flu really kicked my arse. A few of us were crook, but that is not an excuse why we lost."
Tevaga was confident with a narrow 10-6 halftime deficit, before they fell away in the third quarter as the Eels capitalised on errors to grab two quick tries.
"It's pretty much the story of our season," said Tevaga. "We started off the second half pretty poorly, and you can't afford that against the better teams. For the majority of the game we were right in it, just little key moments let them slip away."
There were positives amid the frustration. Tevaga said plenty of players "had a real crack", identifying Euan Aitken as particularly impressive.
"There are areas that we need to tidy up but at least we are putting ourselves in games, not just rolling over and getting our arses kicked," said Tevaga.
As well as avoiding the dreaded wooden spoon, the middle forward hopes the team can maintain high standards as they try to eke something out of the remaining seven games, which include three in Auckland.
"The goal for us is to finish the year strongly," said Tevaga. "We haven't had a great season. But we have a few home games and that atmosphere against the Tigers was unreal. I hope we can experience that again and what will help that is if we put in good performances."