Unfortunately, it is exactly like a blank cheque. All surveyors working for the neighbours (Adjoining Owners) are paid by the hour. However, fees should still be 'reasonable' under the Act. In my experience, if you are in London, you are looking at £1100 - £1500 for their surveyor. The average Award takes 6-8 hours and average hourly rates are anything from £120.00 - £250.00. Their surveyor will likely be on the higher end if they have recieved unsolicited letters from unscrupulous surveyors touting for business, off the back of the approved planning application lists.
A Third Surveyor is appointed but only used if both surveyors cannot agree on a way forward. The Third Surveyor can split his fees between both parties, so it's a risk that adjoining owners surveyors often do not like to take because they will have already assured your neighbours that they wont have any fees to pay, to get them to sign their Appointment Letter. For works such as yours, the Third Surveyor isnt often used, it is more common on complex projects such as new basements etc.
It really is a terrible system and quite stressful for the Building Owners (the ones carrying out the works).
Another thing to note is that it is often preferable to take the dormer to the boundary line to enable them or the next owners to build their own dormer right up against it. If you set it back, it is difficult for them to do one in the future as there is no workable space for their Contractor to finish off the side cheek of their dormer and weatherproof (unless they move it back substantially).
Party Wall Awards can take some time, so get the process started now (you have 12 months to start, but not complete the works once it is served). It adds to the stress when you have a contractor desperate to start and their party wall surveyor is dragging his heels.
Personally, I'd just swallow the costs of their surveyor and not put in an amended planning application. If you've got permission granted its unreasonable of them to use the appointment of a surveyor to blackmail you with!