Santour's note is not very much different with other instruments. The only main difference would be mezrab's signs. Almost each master has its own signs but there are similarity. Most of these signs are the same in all santoors book. For more information please visit this link.
For example Payvar music notation is a little different with Ardavan Kamkar music notation and you need to practice so you could play both of them.
As a professional santour player you should be able to play every master's notation (Somaei, Payvar, Meshkatian, Kamkar,etc) masterfully.
You might hear a song somewhere and want to play that on you santour. First of all you have to distinguish what is the tune of the song (listen to the song several times and carefully), then you have to try to find the notes, if you couldn’t do that try searching the note in google.