You don't say whether this is NEC3 or NEC4, as there is no requirement under NEC3 for a payment application to be submitted, although this is a common amendment, however the Project Manager is required to consider any application submitted on or before the assessment date.
From what you have said it looks like the Contractor expressly disagrees with the amount that the Project Manager previously certified. The Project Manager, however, makes an assessment based upon the Price for Work Done to Date, the definition of which is different depending on what main option is used.
Under the requirements of the 'Construction Act' the Project Manager is acting as a 'specified person' and is obliged to notify the amount due and state the basis upon which that sum has been calculated. Provided that has occurred then the only recourse for the Contractor is to formally dispute this, although hopefully you will be able to meet to discuss the difference between the amounts applied for and the amounts certified.