I speculate that £4424 was the net amount of income received after CIS deductions, and that the gross income from self employment was £5530 less 20% tax. But I could be wrong. The CIS deduction rates tend to be either 0%, 20% or 30% depending on whatnot. I suppose he could have changed from one to the other part way through, giving rise to an average 25% rate but I would bet not.
He almost certainly does not have a P45 to present to Tarmac. To be valid it would have to have been issued by a previous employer for which the employment ceased in the current tax year. So, without a form P45 I would expect tarmac to have required from him a P46 on which he would have made a declaration regarding whether this is his only or main job, etc. That would have determined his initial PAYE coding notice with Tarmac, which HMRC may subsequently have amended for any number of reasons. That coding notice may have been on a cumulative or month 1 basis.
The short answer is: without knowing his PAYE code applied by Tarmac, it is not really possible to state whether he will be entitled to a tax rebate. That said, I would guess that he almost certainly will be entitled, mainly because his net taxable income after allowable deductions will be rather less than the £5530 that has been taxed in full at 20% and on which there should be no NI charge at that level.
Not quite sure of his class 2 NIC liability. Strictly he should register as liable, but then maybe can claim exception on the basis of low earnings. Registering for class 2 NIC would put him on the self assessment tax return radar, despite that he probably has no statutory requirement to notify chargeability to Income Tax under S.7 Taxes Management Act 1970, by reason of the CIS deductions. Interesting, not really thought of that before. However, filing a self assessment tax return is the obvious route to getting the refund.