Plates which are separating let molten rock from the mantle up, where it cools hardens. Any rock which can be magnetised (iron) is aligned with the Earth's magnetic field when molten, and gets fixed that way. The magnetic field swaps every 10,000 years or so [https://en.wikipedia.org/wiki/Geomagnetic_reversal], so you get a stripey effect.
Working our more precised dates for the magnetic swaps is a matter of slow and painstaking correlation with other bits of evidence: dating of radioactive elements, tree rings, rock layers, the temperature of the Earth, composition of gas bubbles trapped in rock and ice.
Latitude when combined with geometric constraints of seafloor strips and correlated trans-ocean rock formations build the overall picture.
In addition the oldest seafloor is 220 million years old or 5% of Earths lifetime. Paleomag measurements go back ten times longer.
There may be tens of thousand of research papers behind each map shown in the OP. It is like solving a puzzle. At location X, Scientist A finds some clues in plate tectonics, Scientist B finds something in geochemistry, and Scientist C finds something in fossil records. Then they piece them together and if these stories all tell the same thing without a serious conflict, you can construct a point on that map. Now imagine doing this for thousands of different regions involving several generations of scientists, you get nice maps like these.
This Wikipedia page would be a nice read: https://en.wikipedia.org/wiki/History_of_Earth.