My guess is the Lions wanted to re-sign Benito Jones but at a contract level that didn't satisfy Jones. It wouldn't even surprise me if the Dolphins contract offer was very similar to the Lions offer (assuming there was an offer) but he thought the Dolphins were a better opportunity for him moving forward.
Benito Jones made some plays in which he showed high level ability or close to that. Yet, overall, Jones wasn't consistent enough for the Lions to Tender him as a RFA.
With Benito Jones no longer an option for the Lions as long as he's on the Dolphins roster, the Lions should try to add another DT who would compete for a backup DT roster spot. Levi Onwuzurike and Brodric Martin remain huge question marks.