I can share some insights about how classes work in QuickBooks Online.
The class that you've added to your employees will only affect the current and future payroll taxes. The previous year's payroll taxes won't be allocated to the class that you've just assigned to your employees.
You may need to delete and then recreate your past payrolls so that the class will be added. Before diving in, please take note that you can only create unscheduled checks for the current pay period all the way back to pay periods dating 6 months ago. Here's how to do it:
Select Payroll from the sidebar menu.
Go to the Employees tab.
Select Run payroll.
Find the employee you want to pay, and then select Create another check.
Enter the appropriate information based on the deleted paycheck.
Select Preview Payroll, then choose Submit payroll.