The news comes via Publix's Twitter account yesterday, responding to a customer who asked about the lack of support for Apple's mobile payments system.
Good Morning. Our stores are currently rolling out this technology to all of our stores. If your store does not currently accept Apple Pay it should within the coming weeks. ≈ Monique— Publix (@Publix) May 29, 2019
Not all of Publix's Twitter support agents appear to have been briefed on the news, however, as just in the past few hours other responses to customers have simply offered to "share your suggestion" with the customer service or payments team.
There have been scattered reports of Publix testing Apple Pay in a few stores for a while now, but it looks like a full rollout is finally underway.
Update 8:00 PM: In a follow-up Tweet, Publix now says its initial response was "incorrect." Publix is actually rolling out its own Publix Pay system.