Ben Affleck’s birthday celebration was a quiet but close affair.

On the evening of his 49th birthday on Sunday, Affleck shared a “quiet celebration” alongsideJennifer Lopezand her 13-year-old twins,Max and Emme, a source close to Lopez tells PEOPLE in this week’s issue.

“Jennifer had a cake for him. Ben is not one for big celebrations, so he thought it was perfect,” says the source. “It was exactly what he wanted.”

Earlier on Sunday, the Oscar-winning director and actor enjoy some time alone with his kidsViolet, 15,Seraphina, 12 andSamuel, 9, whom he shares with ex-wifeJennifer Garner.

For more onJennifer LopezandBen Affleck’s rekindled romance and other top stories, listen below toour daily podcast PEOPLE Every Day.

Before meeting with Affleck, Lopez and Emme were spotted at producer Jennifer Klein’s home for her annual Day of Indulgence event where the singer and the teenager were spotted picking out jewelry for Violet and Seraphina.

The couple, whorecently vacationed in St. Tropez for Lopez’s birthday, are getting serious as Lopezplots a movefrom Miami to Los Angeles, where Affleck is based. An insider previously told PEOPLE that Emme and Max are"onboard with starting fresh in Los Angeles."

“They are slowly getting to know Ben,” the source added. “Everything seems to be running smoothly. It’s very obvious that Jennifer is serious about Ben. She hasn’t looked this happy for a long time.”

Elder Ordonez/SplashNews.com

Jennifer Lopez and Ben Affleck

Never miss a story — sign up forPEOPLE’s free daily newsletterto stay up-to-date on the best of what PEOPLE has to offer, from juicy celebrity news to compelling human interest stories.

A source told PEOPLE in May that their relationshipis different this time around. “Time has passed, and they are each in a different place with children,” the insider said.

For AffleckandJennifer Lopez, pick up the latest issue ofPEOPLE, on newsstands Friday.

source: people.com