It looks like the end-credits scene in Ant-Man, where Falcon and Captain America find Bucky is not the start of Captain America: Civil War. As evidenced by Cap's clothing, that scene looks to pick up in the middle of Civil War, which would indicate that parts of Ant-Man and Civil War are occurring simultaneously.
CAPTAIN AMERICA: CIVIL WAR SYNOPSIS
Marvel’s Captain America: Civil War finds Steve Rogers leading the newly formed team of Avengers in their continued efforts to safeguard humanity. But after another incident involving the Avengers results in collateral damage, political pressure mounts to install a system of accountability, headed by a governing body to oversee and direct the team. The new status quo fractures the Avengers, resulting in two camps—one led by Steve Rogers and his desire for the Avengers to remain free to defend humanity without government interference, and the other following Tony Stark’s surprising decision to support government oversight and accountability. Get ready to pick a side and join the nonstop action playing out on two fronts when Marvel’s Captain America: Civil War opens in U.S. theaters on May.