Acuña left Weather Report in 1978, and became a session musician in California, recording and playing live with (amongst many others) Paul McCartney, Joni Mitchell, Ella Fitzgerald, Elvis Presley, Michael Jackson, Chick Corea, Whitney Houston, Plácido Domingo, former Weather Report bandmates Wayne Shorter and Joe Zawinul, Herbie Hancock, Carlos Santana, Antonio Carlos Jobim, Beck, Roberta Flack, U2, Al Jarreau and Marcos Witt.

He appears on recordings by musicians as culturally diverse as Lee Ritenour, Johnny Clegg, Roy Orbison, YellowJackets, Lalo Schifrin, Milton Nascimento, Don Grusin, Dave Grusin, The Brecker Brothers, Arturo Sandoval, Vladislav Sendecki, Paquito d'Rivera, Gonzalo Rubalcaba, Brad Mehldau, BoDeans, Paco de Lucia, John Patitucci, Sadao Watanabe, Lyle Mays, Diana Ross, Sérgio Mendes, Robbie Robertson, Jackson Browne, Bette Midler, Emiel van Egdom, Jennifer Nettles, Christina Aguilera, Seal and Chris Botti.

[3] In the 1980s Acuña also recorded and toured with the Christian jazz band Koinonia, which featured session musicians Abraham Laboriel, Justo Almario, Hadley Hockensmith, Harlan Rogers, and Bill Maxwell.

The Winans, Andraé Crouch, Madonna, He played on Willy DeVille's Crow Jane Alley album and in 1987 he teamed up with Elvis Presley's TCB Band for the Roy Orbison TV special "A Black and White Night".

He played percussion on Blondie's number one hit "The Tide Is High" and also recorded more than 300 movies under the direction of Lalo Schifrin, Dave Grusin, Michel Legrand, Bill Conti, James Horner, James Newton Howard, John Williams, Alan Silvestri, Michael Giacchino, Christopher Beck, Maurice Jarre, Steve Jablonsky, John Powell and Heitor Pereira.