When does the warranty start for a refurbished Mac Mini?

The Mac does not have to be registered to check the warrant status.

And, iirc, your warranty starts when you pick up the computer.

Legal - Hardware Warranties - Apple

Meanwhile, you will have fourteen days to return it, no questions asked, if you bought it directly from Apple.

Returns & Refunds - Shopping Help - Apple

Please read the information completely in the links provided, they have the answers you are looking for!

Also, I STRONGLY suggest that you buy AppleCare for your MM. It is much less expensive than paying out of pocket in the event of a repair after the original 1 year warranty period. Yes, even Apple refurbished products are eligible for AppleCare however your time frame to buy it is very limited.

By the way the warranty is exactly the same as it is for new Macs. Terms, duration, AppleCare eligibility, everything... exactly the same.

Follow-up:

My saved emails show my new m4 Pro Macbook Pro 14 shipped on March 12. When I do System Settings > General > AppleCare and Warranty it show the warranty expires on March 12, 2026.

Use this Apple page to check:

Check Your Service and Support Coverage - Apple Support