Hayne ran for a team-high 120-all-purpose yards in a stunning debut highlighted by his 53-year dash at running back in the 23-10 pre-season loss to the Houston Texans.
The 27-year-old finished with 63 rushing yards from five runs, returned two punts for 24 yards and produced a 33-yard kick-off return, sending Twitter into meltdown in both the US and back home in Australia.
Veteran Aussie journalists had to be reminded not to cheer their man by Texans officials in the press box and American scribes were effusive in their praise of the dual Dally M medalist.
But Tomsula, who will cull his 90-man squad to 53 players next month, called for calm.
"I'd just like to temper everything," Tomsula told reporters.
"We don't need to put undue things on Jarryd, undue expectations.
"It's not necessary, to me, to put that on his plate right now.
"I just want him to stay focused on getting better. The guy's a world-class athlete (who has) played professional sports for seven, eight, nine years."
Watch it again! @jarrydhayne_1 breaks loose for a big 53-yard gain. #SFvsHOU http://t.co/LnPrLrsVJS pic.twitter.com/7TlH600mHh
— San Francisco 49ers (@49ers) August 16, 2015Hayne is one of six running backs trying to make the 49ers roster.
Carlos Hyde is the number one, Reggie Bush will be the back-up and Kendall Hunter is probably still third in the pecking order.
That leaves Hayne, fourth-round draft pick Mike Davis and Kendall Gaskins fighting for one spot.
It is almost unheard of for an NFL team to take five running backs into a season but Hayne’s good work as both a kick and punt return man against the Texans could see Tomsula make an exception and take Hayne as his number five.
Tomsula made it clear he needs to see more from the rugby league superstar in the remaining trial games against the Dallas Cowboys (Monday AEST), Denver Broncos (August 30 AEST)) and San Diego Chargers (Sep 4 AEST).
"We're definitely looking for the growth to be from Week 1 to Week 2 … and then (Week) 2 to (Week) 3," Tomsula said.
“After Week 3…you’re running out of time. We want to see the growth between these two games."“The things that excite me about Jarryd Hayne, the things that we've got to stay on, is when you get into those tighter quarters and see those little creases.
"That's where the improvement is. That's just where he needs to keep working. Not that he's bad at it - he's not, but we've just got to keep improving there."
The 49ers open their regular season against the Minnesota Vikings on Tuesday, September 15.