"From what I understand, everything was what we thought in the beginning. They fixed what they had to fix."
Williams will wear a splint on his thumb and be re-evaluated in six seeks. His physical activity will be limited to restricted weight lifting and conditioning.
Corbin exchanged text messages with Williams before Utah's game against Phoenix.
"He said he slept very well he slept like a baby," Corbin said. "… [But] he's happy it's over."
Williams will remain in New York "for a few days" while recovering from the surgery and having the splint made for his hand.
He will rehab in Salt Lake City and, eventually, accompany the Jazz on the road, Corbin said.
Williams, who averages 12.9 points and 6.7 assists, was injured on Dec. 22 at Miami.
In Williams' place, veteran Jamaal Tinsley has been starting.
In the Jazz's first five games without Williams, Tinsley averaged 6.8 points and 5.6 assists. He made 13 of his 28 field-goal attempts.
Sprained ankle sidelines Kanter
The Jazz also played Phoenix without backup center Enes Kanter, who missed his first game of the season because of a sprained ankle.
Kanter is listed as day-to-day. His availability for Saturday night's game at Denver is uncertain.
Kanter suffered the injury in the closing moments of Wednesday night's 106-84 win over Minnesota after he scored 15 points and grabbed eight rebounds.
He averages 6.7 points and 4.3 rebounds in 15.3 minutes this season.
According to Corbin, Kanter's absence probably translates more minutes for Al Jefferson, Paul Millsap and Derrick Favors.
Jeremy Evans, who played only 95 minutes in Utah's first 33 games, could also become more involved.
Another possibility: small forward Marvin Williams could be asked to play power forward.
Jefferson turned 28 on Friday, but there was little celebration.
"We got a game," he said before tip-off against the Suns. "I figure I'll celebrate some other day. When I get some free time, I'll celebrate a little. But I didn't do nothing today."
Not including exiled veteran Raja Bell, Jefferson is the fifth-oldest player on the Jazz's roster behind Tinsley (34), Earl Watson (33), Mo Williams (30) and Randy Foye (29).