When you assigned processing class to a wage type, It will be processed according to the logic has been written in the rule but there are many other conditions where it is a monthly exemption or annual exemption what is the limit for exemption, whether wage type is valid or not all these conditions will be cross checked with the help of tax code only since tax code is maintained against to the wage type at table level and some thing has been coded in the tax code as well.
So even though you have maintained processing class according to the requirement you have to maintained tax code as well.
Regards
Venkatesh