For my employee, when I add a new employee leave record to their record, it does not reflect inside the pay slip.

Ensure that you click Update to Payroll and reprocess the payslip again for the leave balance to reflect in the payslip.

Example: Sample Employee took 10 annual leaves during the month of April

Update to Payroll -> Tick the payroll month you want the leave to reflect in -> Update

Reprocess the payslip: 

Payroll -> Edit -> Select employee to process -> Process Pay -> Ok

The report should reflect the leaves taken