In Germany, Tax class changed to 3 two month back but I am still getting salary as tax class 1. How much transition time generally take for class transaction to reflect my monthly salary.
This is purely an issue with your employeer,so quite hard to give an exact figurehere. Anything above 2 months, contact HR.
Some employers just query the Elstam database at the beginning of the year. If you have changes during the year, you have to tell them about the update so they can request your Elstam file again.
But don't worry too much about it. If you file your taxes, everything will be corrected by the Finanzamt so in your case you will probably get a bigger tax return than you are used to.