Under ECC clause 62.2, each quotation for each compensation event comprises proposed changes to the prices (in your case the total of the activity schedule), and any delay to the completion date and key dates. The contractor also has to consider whether any sectional completion dates are affected if secondary option X5 is incorporated. In the main, clause 63.1 tells you how to assess the money side of this and clause 63.3 the time side.
Your question was specific about on-site staff. There is no extension of time as such in the ECC, but each compensation event may or may not affect any key dates, sectional completion or the completion date of the whole of the works. Even if it does not, the on-site staff might work nights or weekends, or additional staff might be brought onto the site to deal with the event, being more cost effective than changing these dates.
So, you actually need to look at the, ‘effect of the compensation event upon .... Defined Cost’ as stated in clause 63.1. Ask the question: how is defined cost (which includes on-site staff) affected by this compensation event? If the answer is that they are not − no overtime, no additional staff or no extended stay on site − then that is your answer. ‘Effect’ becomes the key word to focus on here.