The words used are ‘the total time recorded’ therefore the time has to include in that total the hours recorded for other matters such as sick time training and holiday time. Otherwise it would not be the total time recorded.
Any other drafting intention would require different words to be used to limit the hours recorded to something less than the total, by reference to ‘billing hours’ or some other such wording. Such a wording was, quite deliberately, not chosen.
This is explained in page 83 of volume 4 of the user guide for the NEC4 PSC. This makes clear that the cost recording system must identify any non-productive and non-fee earning time as part of the total.