The instrumental jazz song that Tinker puts on his record player after shagging Julia Foster's character is Tony Kinsey's Bassman from his album "An Evening with Tony Kinsey" while the LP that Tinker is holding is not Tony Kinsey but what looks like a British rock 'n' roll band.
At around the 41 minute mark the jazz track that Tinker plays for Julia Foster's character is "Bassman" from the LP "An Evening With Tony Kinsey", by Brit jazzer Tony Kinsey. But the LP sleeve he has in his hand is the album "Out of the Afternoon" by the Roy Haynes Quartet. Both are very cool records though.