Investigators allege yellow cards, which are universally issued as cautions by referees for foul play, were manipulated during games played on November 24 and December 9.
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.
Davila got his yellow card on November 24 for arguing with the referee and was booked on December 9 for kicking the ball away when the opposition team had been awarded a free kick.
Only Baccus was booked in the April 20 clash, while none received a yellow in the May 4 outing – but police allege only “unforeseen circumstances” stopped them.
NSW Police Assistant Commissioner Michael Fitzgerald said the players had “betrayed the trust of their supporters and the code”.
“A$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,” he said.
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.
UK officials tipped off local authorities after spotting suspicious betting patterns.
No evidence shows suspicious betting within Australia, they said.
Macarthur FC chief executive Sam Krslovic said the club was caught off-guard by the charges but it would work with authorities.
“The club is shocked and aware of the arrests ... integrity of our game is a foundation pillar and we will work closely with all relevant agencies on this matter,” he said.
Davila was charged with two counts of engaging in conduct that corrupts the betting outcome of an event, facilitating conduct that corrupts the betting outcome of an event and participating in a criminal group.
Police allege he was taking instructions from another man, believed to be based in South America, to organise the players to receive yellow cards in return for payment.
The other two players were charged with engaging in conduct that corrupts a betting outcome of an event and participating in a criminal group.
The gambling offences all carry maximum 10-year jail terms.
Sports Integrity Australia said it acted on information from a UK agency working with the Australian Criminal Intelligence Commission on the investigation.
The Australian Professional Leagues said work to protect sporting integrity “must be unwavering”.
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.
Davila, who won the Johnny Warren Medal in 2021, joined Macarthur ahead of the 2021-22 season and was best on ground when the team won the 2022 Australia Cup final.
His wife Lily Pacheco died in 2022 from a disease affecting blood flow to the brain and Davila has said that he “didn’t care about football” after her death.
