Couple of points here:
- no such thing as day rates under NEC. If you have pre-agreed set rates for people cost and this is intended to replace the section 1 of the schedule of cost components than that is the rates you should use. However, it should have been made clear at tender stage what these rules are.
- fee percentages are then applied in accordance with the rules of the contract. Sub-subcontract fee applies to any sub-subcontracted elements, and everything else would attract the direct fee percentage.