Phillips said on Monday that his contract with French club Bayonne had been terminated, and he now intends to issue legal proceedings against them.
Bayonne have now also confirmed 31-year-old Phillips' exit after he allegedly turned up drunk for a player video analysis session at the Top 14 club earlier this month.
Phillips trained with Wales in a public session at the Millennium Stadium on Tuesday - which was watched by a crowd of just under 10,000 - and he looks set to start the autumn series opener against South Africa on November 9.
"The players have been quite respectful of Mike and not really asked him about what happened," Warburton said.
"I am sure he is sick of answering all the questions, and we have kind of left him alone.
"But whenever he has been in a Welsh shirt he has always played great, so I am sure he will put things behind him and perform this autumn."
Warburton's public backing for his fellow British and Irish Lion follows that of Wales coach Warren Gatland, with the 77 times-capped scrum-half remaining a pivotal player in a squad preparing to face the Springboks, Argentina, Tonga and Australia next month.
Bayonne, meanwhile, issued the following statement on Tuesday after an episode that also saw Phillips' team-mates Dwayne Haare and Stephen Brett face the club board to answer for their involvement in the same incident.
Phillips sat out last Friday's 24-19 victory over Montpellier, but Brett started the match and Haare was included on the bench.
In their statement, Bayonne said: "Mr Philippe Ruggieri, chairman of the management board of the Avion Bayonnais, specifies to have met on Saturday, October 26, 2013 Mr Mike Phillips before ultimate reflection.
"He indicates that the contract of employment linking the club to Mike Phillips came to an end in an anticipated way (this contract normally had to arrive forward on June 30, 2014).
"The legal representative of the club wishes to specify that the facts which the media stated do not concern in the same way the three players whose identity they reported."
Phillips was accused of being intoxicated when the squad met on October 11, the morning after Grenoble had been defeated 37-6 by Bayonne in an Amlin Challenge Cup pool game.
Phillips claims he then learned of his dismissal from an interview in a French newspaper on Monday morning, when Bayonne chairman Alain Afflelou described Phillips' alleged behaviour as "treason".
In his statement, Phillips said: "I am extremely disappointed and frustrated by the decision taken by Aviron Bayonnais Rugby Club to terminate my employment.
"I was also disappointed by the fact that I officially heard about my dismissal through an interview given in a French newspaper.
"As a result of discussions with my legal team in France I have now instructed them to issue proceedings against Aviron Bayonnais Rugby Club through the French judicial system."
Phillips was fined and suspended for 10 days by relegation-threatened Bayonne for an off-field incident last year, and he was briefly banned from the Wales squad in 2011 following a confrontation with a doorman in Cardiff.
But there were no outward signs of his Bayonne issues as Phillips played a full part in an hour-long session conducted by Gatland and coaching assistants Rob Howley, Shaun Edwards, Robin McBryde and Neil Jenkins.
And Warburton has made an immediate statement of intent as Wales look to start redressing the balance in terms of a miserable record against major southern hemisphere opposition.
"Getting that win against a southern hemisphere side is something we have been looking forward to for such a long time," he said.
"We have got to the stage now where we have done well in the northern hemisphere, but I always look at the England team of 2003 that managed to play the Tri-Nations sides and beat them all.
"As a group of players, that has to be the next step for us.
"We keep doing well in the Six Nations, and that is your bread and butter.
"But it is getting to the stage now where we have to perform in the autumn and start taking the southern hemisphere scalps."
- Sports & Recreation
- Mike Phillips