On January 30, the Cronulla Sharks player was diagnosed with grade-four medulloblastoma after complaining of constant headaches earlier in the month.
On Monday, Kula underwent surgery to install a shunt that will reduce the excess fluid putting pressure on his skull.
The 21-year-old is expected to return home next week before starting chemotherapy and radiation treatment later this month.
A GoFundMe page was set up on Saturday night and has reached over $13,000 on Friday with the likes of Sydney Roosters forward Siua Taukeiaho and Sharks players Bronson Xerri, Braden Hamlin-Uele, Jack Williams and Scott Sorensen contributing.
"I'm shocked. I just want to thank everyone for donating," Kula told the Sydney Morning Herald.
"Everything is all good at the moment. Hopefully I can go home next week."
Kula was born in Auckland and moved to Australia in 2014, where he's
progressed through the ranks at the Sharks. This year, he was on a train and trial contract for the opportunity to break into the Sharks' top-30 NRL squad.
Kulu has won the NSWRL Matthews Cup Player of the Year in 2015 and a part of the Sharks championship-winning Jersey Flegg team in 2018. He also represented the Junior Kiwis.
Kulu's dad Solomon said the family is grateful for everyone's support.
"We want to thank everybody for their well wishes and prayers," Soloman told the Sydney Morning Herald.
"Right now with what Fine's going through as parents, it is out of our hands, it’s in somebody else’s hands. All we can do is pray for the doctors and nurses and the people looking after Fine to get him through.
"The thing I’ve been doing in answering people’s messages is just saying thank you. That’s all we can say."