Taumalolo has been fined $2,500 by the club over the incident.
"Thanks to the RLPA for supporting the players. What they have done for us players behind closed doors is so big for us. It makes us worry more about footy that off-field dramas," Taumalolo said.
Thurston said Taumalolo was a deserved recipient.
"It is the biggest award you can win in rugby league to be voted by your peers as the best in the game," Thurston said.
"He has had an outstanding season I am very proud of him and what he has achieved this year.
South Sydney playmaker Cody Walker won RLPA rookie of the year.
Sydney Roosters forward Nat Butcher won the NYC player of the year award.
Greg Inglis was named as Australia's representative player of the year, Jesse Bromwich the same honour for New Zealand.
James Graham won the rest of the world representative player of the year.
Australia's Samantha Bremner and New Zealand's Georgie Hale were respectively named national women's players of the year.