Dávila, who now leads Australian side Macarthur FC, and fellow players Kearyn Baccus and Clayton Lewis have been arrested over their alleged involvement in the betting fix, which police say has led to hundreds of thousands of dollars being paid out in winnings.
Authorities are still chasing a fourth player allegedly involved in the scheme, threatening to extradite him if he does not return to New South Wales to face questioning.
They also allege unsuccessful attempts were made to do the same thing during matches on April 20 and May 4.
Macarthur played out a 1-1 draw with Melbourne Victory on November 24 before beating Sydney FC 2-0 on December 9.
All three were booked in the December 9 game against Sydney.
The team beat Sydney 1-0 on April 20 before being thrashed 4-0 by the Sky Blues on May 4.
NSW Police Assistant Commissioner Michael Fitzgerald said the players had "betrayed the trust of their supporters and the code".
"Yellow cards and the subsequent penalties that arise out of those yellow cards could change the result of that game," he told reporters on Friday.
"$10,000 may seem a lot of money to a young sports person, (but) that is incredibly insignificant when you consider the damage that being charged with this offence and convicted results in."
The southwest Sydney club said it was "shocked" by the allegations of yellow-card manipulation among its players, which came after a six-month police investigation.
NSW Police said the probe was launched in December 2023 with the help of officials in the United Kingdom after suspicious betting patterns were identified.
Macarthur FC chief executive Sam Krslovic said the club was caught off-guard by the arrests but it would work with authorities.
"The club is shocked and aware of the arrests of three A-League players by NSW Police as a result of international law enforcement co-ordination focused on betting corruption related to alleged yellow card manipulation in games," he said.
"Integrity of our game is a foundation pillar and we will work closely with all relevant agencies on this matter."
Davila was arrested on Friday at South Coogee, in Sydney's east, when police executed a search warrant as part of the investigation.
Lewis was arrested in Parramatta and Baccus was arrested in Campbelltown.
Davila is expected to be charged with two counts of engaging in conduct that corrupts a betting outcome of an event and two counts of facilitating conduct that corrupts a betting outcome of an event.
The other two players will be charged with engaging in conduct that corrupts a betting outcome of an event.
Authorities said on Friday afternoon the players had yet to be charged and were at police stations, but were likely to be bailed before initial court appearances.
Sports Integrity Australia said it acted on information from a UK agency working with the Australian Criminal Intelligence Commission on their investigation.
Football Australia said it was made aware of the arrests on Friday morning and was cooperating with the investigation.
The Australian Professional Leagues, which runs the A-League competitions, also acknowledged the arrest as a result of "international law enforcement co-ordination".
"The work to protect the integrity of our game must be unwavering and we are liaising closely with all relevant agencies on this matter," it said in a statement.
Macarthur FC has been in the A-League Men's competition since the 2020-21 season. The team finished this regular season in fifth before being knocked out by Sydney FC in an elimination final.
