Delta 2MM and Diamond Medallion. 99% of the time when I fly TATL I'm on Delta metal. This time I'm not: DL flight number, KL operated flight on the 787-10 (so coach and business, no Premium Select or equivalent) from ATL-AMS.

I understand that sometimes KL offers paid upgrades at or after checkin. Can someone knowledgeable explain how this works? I assume I check in using KLM's web site (and not Delta's), and then what, it pops up a "would you like to ugprade?" banner or something? Do they offer upgrades to everyone first-come, first-served, or only to SkyTeam Elites, or what?

It looks like right now there are about 11 open J seats so I'm crossing my fingers.