Although Publix has said that they are rolling out Apple Pay to all of their stores, it is being done the same way that Target and HyVee did it where it will be a gradual process.
Apple Pay can be used on the iPhone (iPhone 6-current) and the Apple Watch. By accepting Apple Pay, customers will be able to use Apple Cash as another form of payment too.
UPDATE (05/30/2019) 10:20 PM CDT: Publix has made a new tweet saying that they will be getting Publix Pay and NOT Apple Pay.
— Publix (@Publix) May 31, 2019