Tigers are unbeaten after two rounds in First Utility Super League, having drawn at Hull KR and crushed Wakefield Trinity Wildcats 40-6 in their home opener two days ago.
Solomona, who scored in both games, reckons Tigers are showing good signs, but will need to step up a notch at KC Stadium, a week on Thursday.
Hull have won their opening two matches, at home to Salford Red Devils and in Perpignan against Catalans Dragons and are being tipped as the competitions big improvers this season.
That is a view Solomona shares, which makes him wary of next week’s challenge.
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“They will be pretty good this year,” Solomona predicted.
“Hull have got a good side.
“When we face them we have to do our jobs and do our best, as they are going well.
“I have some mates over there, like Mahe Fonua and Sika Manu, so they are keeping me updated.”
But the former London Broncos winger feels Hull should be just as worried about Tigers, who ran in seven tries in the demolition of Wakefield, including a brace by Solomona.
Full-back Luke Dorn and stand-off Ben Roberts also crossed for Tigers, but Solomona said it was the pack who laid the foundations for the win.
“I think it all comes down to our middle men,” he said.
“They went out there and really did their jobs.
“They ran hard, tackled hard and us outside men then did our jobs as well by just finishing off all that they had done for us.
“It was all the forwards’ hard work; all we needed to do was put the ball down really.”
Solomona did that in spectacular style, with an airborne finish for his second touchdown.
Coach Daryl Powell described that score as “world-class” and “unbelievable”, even for a player noted for his finishing. Solomona insisted: “It’s just what it is.
“I try and get to the try line as much as I can and finish off the hard work from those middle men.
“It’s the least I can do.”
The winger was also impressed with the contribution of veteran Dorn, who created both his tries.
“Luke Dorn is amazing out of the back,” he said of the ex-London and Salford man.
“He’s a great talker, a great communicator and he helps Galey [Luke Gale] and Benny Roberts organising our plays too.
“He is outstanding.”
Meanwhile, Tigers came through the game with no new injuries and coach Daryl Powell was pleased with forward Nathan Massey on his return from a damaged hand.
“He was really good,” Powell said. “It was like he had never been away. I’m really pleased to have him back.”
Powell was happy with the win and performance ahead of this weekend’s Super League break.
He said: “We started a bit slowly, but if we had been a bit more clinical we could have been a bit further ahead.
“There’s a few bits and pieces to work on, but we certainly improved from the week before, which is a good sign.”
Of the week off, Powell said: “I don’t think it matters too much, but the game at Hull is on a Thursday, so I think for us it is more on the benefit side than anything else.”