The Personal Year adds a person's reduced birth month and birth day to the reduced current calendar year, giving a figure that advances by one each year and returns to the start after nine. Practitioners use it as the main timing instrument in the chart, and clients ask about it more than anything else.
The system has never agreed on when it changes. One camp turns it over at the start of the calendar year, on the reasoning that the calendar year is one of the inputs and the figure should change when that input does. The other turns it over on the birthday, on the reasoning that a personal cycle should be personal and should begin where the person did. A third position, taught in some lineages, treats the transition as gradual across the months either side.
The disagreement is not academic. For anyone born after the first of January, which is nearly everyone, the two conventions place them in different personal years for part of every year, and the guidance attached to a one year and a nine year points in opposite directions: one is described as a time to begin things and the other as a time to finish and release them. A client following the wrong convention is being advised to do the reverse of what their practitioner intended.
No argument in the literature settles it, because there is nothing it could be settled against. Which convention a practitioner uses depends on which books they learned from, and the honest thing is to say which one is in use.