There are two elements that determine whether VAT is added on a sales invoice - those are the VAT settings within the Client Entry record and the Rate Code entry itself.
If Vat is applied against the client you need to ensure their Client Entry record is set with the appropriate rate of VAT. Also check the Rate Code Entry for the rate code(s) you have used on the timesheets for the invoice to ensure the Apply Sales Tax box is checked (it is worded as Tax as Etz is an international system - please note this setting does not have anything to do with PAYE tax at all).
If the timesheet is validated then a change is made to the VAT components it will not update automatically unless you refresh it (only Open or mid-process timesheets will pick up the change). This can be changed by going into either the timesheet and clicking Update (this instructs the system to look for changes) or via the Invoice Edit option (within the Sales Invoice menu).
If you select the timesheet then click Update any VAT changes will be applied: