FAI sporting license holders may be tested at any time during FAI competitions. If you are selected for testing, then as for any other sport, you must comply with the instructions provided to you by the testing agency. A refusal to test is considered to be a failed test. It is unclear at this time if this will be delegated to CIAM's aeromodelling commission, nor is is clear if "helpers" will fall into the same category as competitors.
The World Anti-Doping Agency (WADA) publishes the list of prohibited substances on its website http://www.wada-ama.org/. If you have been prescribed a medication by your doctor which is on the prohibited list, you require a Therapeutic Use Exemption (TUE) form to be filled out by your doctor and send this to the FAI at least 21 days prior to the international event.
It should be noted that other prohibited substances are often found in over-the-counter medications that do not require prescription. It is therefore advisable to check the list prior to using these medications. Ultimately the competitor is responsible for what is in their system, with the possible punishment for a positive (or failed) test usually being a 2 year ban from the sport.
Refer to the FAI's anti-doping website as well as WADA for more information regarding this.