From your question I am assuming that you are using NEC3.
Under NEC3 main options A and B, the cost of subsubcontractors is, as you have said, applied to the relevant component under the Shorter Schedule of Cost Components (SSCC) and the subsubcontracted fee is applied to this Defined Cost.
What isn't correct in your understanding is the application of 'fee on fee' as subsubcontracted work only has the subsubcontracted fee percentage applied to it, as per the definition of (main option A and B specific) Defined Cost and Fee, without first applying the Subsubcontractor fee. This is a Subcontractor 'commercial risk issue' under these forms.
Where main options C, D or E are used then the definition of Defined Cost means that subsubcontracted costs are treated differently and are applied in accordance with the definition at 11.2 (23), with other costs applied to the Schedule of Cost Components (SCC).
Under NEC3 main options A and B, the cost of subsubcontractors is, as you have said, applied to the relevant component under the Shorter Schedule of Cost Components (SSCC) and the subsubcontracted fee is applied to this Defined Cost.
What isn't correct in your understanding is the application of 'fee on fee' as subsubcontracted work only has the subsubcontracted fee percentage applied to it, as per the definition of (main option A and B specific) Defined Cost and Fee, without first applying the Subsubcontractor fee. This is a Subcontractor 'commercial risk issue' under these forms.
Where main options C, D or E are used then the definition of Defined Cost means that subsubcontracted costs are treated differently and are applied in accordance with the definition at 11.2 (23), with other costs applied to the Schedule of Cost Components (SCC).