Hmm, is this in a contract. I would suspect, if it is anything like our contracts,that it is an agent of the contractor whose responsibility is to be onsite (at least part of the time) and manage site activities for the contractor. However, I have seen contractors whose construction management teams responsible for specific project nearly never show up onsite, this however inevitably always leads to problems for the project and attempts by the contractor to claim they did not have management onsite during some work activity and can not be held responsible (FWI this never works, as the contracts specify the contractor shall be responsible for all work being conducted onsite by their personnel and subcontractors, and a contractor's representative shall be onsite at all times when such work is being conducted to supervise such work activities).
If "site agent" means the same thing as "construction site supervisor", the main business of the job is co-ordination and management. He or she is the undisputed boss of the construction site.
A construction site supervisor must pre-order the materials into the job site in time for the skilled trades to finish their work according to a schedule. When the trades order materials, the construction site supervisor is responsible to inform the trades that the materials are on site and sometimes to store them safely until they can be used.
He or she must make certain that the trades come onto the site in the correct sequence, in a timely manner so as not to interfere with other trades, and that the work is continuing and finishes on schedule as well as progressing in a timely fashion.
Where there is a dispute between trades, the construction site supervisor is expected to make a ruling that will solve the situation, and will probably cost the owners money. This includes removing unruly trades from the site or firing and replacing contractors if their trades do not perform adequately.
When the trades discover faults in the architectural drawings, the construction site supervisor is expected to review the seriousness of the faults and when necessary arrange an immediate meeting with the architects, owners, and affected trades to make necessary changes. For this purpose, it is expected that a construction site supervisor will be reasonably familiar with the restrictions of the local building codes.
The construction site supervisor is also responsible for ensuring that the site is safe for working; and sometimes employs a site safety supervisor to ensure this is accomplished.
I hope this gives you an idea of the scope of the position of construction site supervisor.
There is also a site agent employed by the architectural firm to periodically inspect a construction site to ensure that the architect's plans and specifications are being followed accurately. This person is called a "clerk of works", and must be knowledgeable in both architecture and building technology.