For the second time in as many years, the Jazz & Heritage Festival will serve as a giant kick-off party for the latest Neville recording project.

In 1992, it was the Neville Brothers’ Family Groove; this year, the Fest ushers in Aaron Neville’s The Grand Tour. It follows his 1991 solo effort, Warm Your Heart, which became, 700,000 copies later, the biggest seller in the modern-day Neville family catalog.

Much of Warm Your Heart was recorded in New...