Understanding date of astronomical events
Precession of equinoxes means that the North pole of the Earth is changing its direction. This also means, that the dates of the seasons (seen from outside the Solar System (= sidereal)) are changing. Nirayana calculates the date of Makar Sankranti with adding years to the first Makar Sankranti, but sayana calculates the date of Makar Sankranti relative to stars (sidereal).
In a nutshell: nirayana is on the same date as the first event (first Makar Sankranti), but sayana is on the same event as the first Makar Sankranti (winter solstice). Yes, winter solstice was once on the 14 January.