Normal tax calculates on a cumulative basis. The calculation uses year to date values rather than pay run values. This includes all gross pay and tax paid values to date within the current tax year. The values could relate to your employment or previous employment.
The tax allowances are also cumulative. If the employee has been on emergency or week 1 status, you might find they pay less tax. They might get a tax refund when you change their tax status to normal.
When should you assign an employee normal tax status?
You put an employee on the normal tax status if Revenue tells you to. Revenues RPN certificate will inform you when the tax status is normal or cumulative.