What's happening is called induced magnetism, detailed in a variety of places, including this paper by Kostadinova-Avramova and Kovacheva in Geophysical Journal International:
It is well established that baked clays, when cooling from
temperatures around 700 °C in a weak magnetic field, such as that of
the Earth, acquire a thermoremanent magnetization (TRM) that is
related to the direction and intensity of that field.
When materials are heated above their Curie temperature -- which varies based on the material -- they lose any permanent magnetic properties they had. As the material cools below its Curie temperature, its magnetic particles are influenced by the local magnetic field and the material develops a new, parallel magnetic structure in response.
So your ferrous clay could be picking up a magnetic field from the Earth, from a local electromagnetic field generated by your kiln or other electrical sources, or even a sufficiently strong local magnetic source.
This mechanism is sufficiently well understood that the field of paleomagnetism studies ancient fired clay objects and other materials of known dates to determine the strength of Earth's magnetic field in a given era and region.
History of Earth’s magnetic field exposed in Judean pottery explores one such application of the process:
In a new study published in Proceedings of the National Academy of
Sciences (PNAS), researchers from Tel Aviv University, Hebrew
University of Jerusalem and University of California-San Diego cite
data obtained from the analysis of 67 well-dated Judean jar handles.
These heat-impacted ceramic pots, which bear royal stamp impressions
from the eighth to second centuries BCE, show evidence of changes in
the strength of the geomagnetic field over the years.
“The period spanned by the jars allowed us to procure data on the
Earth’s magnetic field during that time — the Iron Age through the
Hellenistic Period in Judea,” said Erez Ben-Yosef of TAU’s Institute
of Archaeology, the study’s lead investigator.