Yes, the rules are the same for an air-launched vehicle.
From a 2008 paper describing the FAA's approach ("Separation Distances for Rocket Launch Operations" AIAA 2008-7124)
the permit applicant must identify and qualitatively characterize the risks of each of the potential hazards associated with its proposed operation and apply mitigation measures that lower high risks to public health and safety and the safety of property to acceptable levels. For a permitted flight transitioning through the National Airspace System (NAS) on its way to or from space, a potential hazard exists through which the RLV may explode or breakup causing falling debris to impact nearby aircraft. A permit applicant can mitigate the risk to these nonparticipating aircraft by entering into an agreement with the FAA Air Traffic Control to preemptively close the airspace through and below which the RLV operates. However, there is a potential for the falling debris to spread beyond the bounds of this operating area and this mitigation measure on its own would not prevent nonparticipating aircraft from flying at the edge of the operating area. The FAA/AST estimates the risk to the public on board aircraft flying at the edge of a proposed operating area. The FAA/AST reduces the risk to public on board nonparticipating aircraft to acceptable levels by imposing an additional separation distance for aircraft beyond the edge of the operating area. The designation of the additional area associated with this distance is the aircraft buffer zone. The extent of the aircraft buffer zone applied to the edge of the operating area is determined by first assessing the probability of an aircraft located at the edge of the operating area being impacted by debris capable of causing catastrophic damage. Next the computation is repeated at increasing radial distances from the edge of the operating area until the resulting probability is reduced to an acceptable level. Therefore, the size of the aircraft buffer zone directly relates to the threshold value for acceptable risk to the public.
In other words, to get an FAA flight license, you have to work out a set of exclusion areas, and figure out how to protect people from being harmed them.
The criteria are a mix of things:
There are five main underlying assumptions that contribute to the determination of the size of the aircraft buffer zone. The first assumption is that the vehicle utilizes a flight safety system capable of containing the IIP of the vehicle within the operating area regardless of the failure scenario. The effectiveness of a flight safety system is determined separately from the buffer zone analysis during a permit application evaluation and therefore it will not be discussed here, but will instead be assumed to be a sufficiently reliable method for containing the vehicle’s IIP. The second assumption is a probability of failure of one for the mission (i.e. the vehicle is assumed to fail). The third assumption is that, unless restricted from doing so, nonparticipating aircraft will be flying parallel to the edge of the operating area during the permitted flight. The fourth assumption is that a vehicle failure is no less likely to occur at the operating area boundary than anywhere else in the operating area. The last assumption is that the risk to non-participating aircraft must be no greater than one in ten million (1.0E-7).
Initially, the FAA assumes the flight will be a total failure, and works their probabilities based on that. For the early part of the Pegasus program, that was a really good bet; the first flights were more likely to fail than not, though Pegasus XL has a better record. Eventually, you can establish a record and reduce that assumed probability (note this is a 2008 paper):
A. Probability of Failure
The assignment of probability of vehicle failure during flight is one of the determining criteria in sizing the aircraft buffer zone. A lack of flight history and operational experience of a vehicle generally leads the FAA to size the aircraft buffer zone minimum extent based on a maximum credible event. To accomplish this, the FAA assumes a probability of failure (Pf) equal to 1.0 at each point in time in the proposed trajectory of the vehicle, effectively assuming a failure at each trajectory time step. An examination of the collection of resulting failure scenarios then leads to the identification of the worst-case failure scenario, which is then designated the maximum credible event. Whereas intuition may suggest that other, less severe events may be more likely to occur, sufficient flight test data with which to rank the likelihood of occurrence of events relative to each other does not currently exist for most permitted vehicles. Consequently, sizing these aircraft hazard areas based on hazardous events other than the maximum credible event could provide inadequate protection to aircraft. Once sufficient experience has been gained and data has been collected, the FAA will consider more probabilistic or risk-based approaches to sizing these areas. But until that time, the FAA will continue to determine their minimum dimensions based on a maximum credible event.
The launch license is then predicated on protection of those areas:
Once the permittee establishes the operating area and safety clear zone size the permittee must obtain a written agreement with the responsible Air Traffic Control authority having jurisdiction over the airspace through which a permitted launch or reentry is to take place. Among other things, agreements between air traffic control and the permittee reflect the amount of restricted airspace required to maintain acceptable levels of risk to nonparticipating aircraft.
Depending on what kind of airspace it is, that can be done different ways. Notices to Airmen (NOTAMs) are often used, but if the space is otherwise owned (e.g. the military areas off southern California) it's sufficient to reach agreement with the controlling units.
The Coast Guard is the US agency responsible for safety on the surface of the ocean. On the west coast, that would be the 11th District. There is a Local Notice to Mariners process for notification, but it doesn't seen to be used to warn of hazards of flight from Vandenberg. The Falcon and Delta 1st stage impact zones are part of the southern California military restricted zone, so are handled via those controls: You just don't get permission to go there when they're flying.