This was not about the magnetization during firing, but about the much weaker magnetization acquired later, while staying in the same position without being moved.

That weak magnetization happens below the Curie temperature. Actually, any magnetization happens below the Curie temperature. Heating above the Curie temperature just erases any previous magnetization. A material is easier to magnetize immediately below the Curie temperature, but it can be magnetized at any lower temperature. Thus the ceramics that contains iron oxides acquires an initial strong magnetization while cooling down, and a weaker superposed magnetization if it is not moved for a long time. The 2 magnetizations can be distinguished by having different directions, as the pottery stayed buried in a different orientation than when it had been fired.

Only pottery that has not been moved for a very long time acquires a strong enough secondary magnetization. So the test distinguished pottery that has been used recently from pottery that stayed buried for centuries, by the strengths of their secondary magnetizations, not by their primary magnetizations.

A weak magnetization can be erased by heating even below the Curie temperature (which completely erases any kind of magnetization), so this is how they tested. The ferromagnetic materials are divided into hard and soft. The former are used for things like permanent magnets, while the latter are used for things like transformers and inductors.

The difference between hard and soft magnetic materials is that the latter loose quickly their magnetization even at the ambient temperature. Most ferromagnetic materials, which have not been specifically designed to be as soft as possible or as hard as possible, have intermediate softness, i.e. they start to loose quickly their magnetizations at temperatures higher than the normal ambient temperatures, but still much lower than their Curie temperatures. The tested ceramics also behave like this.

We should probably assume that the authors are aware of ceramics, Curie points, and the earth magnetic field. While the article isn't very clear on what effect causes the change in temperature needed to erase the VRM. I suspect is has something to do with how long the object has spent stationary with respect to the earth's field. At least that's my takeaway from having to periodically rotate magnetometers to prevent them from acquiring a bias.