Can the patent fee reduction only apply to the first three years? When does it start?

No.

The fee reduction lasts for six years, starting from the year of application. For example, if you submit a patent application in 2011, it will not be issued until 2013. In 2013, you will pay the annual fee for the third year. The maximum fee will be reduced until 2016, and you will have to pay the original price in 2017.