Does visitor export include the purchase of airline tickets? If so, I would assume that it only counts airline businesses that are established in the country of question.
The UN SNA (2008, p. 42) has this to say:
planes belonging to a domestic airline are always assets of the domestic economy regardless of where in the world they happen to be.
So, conceptually,* we should include in our country's GDP any services provided by any planes belonging to domestic airlines. And so for example, the fare paid in a Ryanair (based in Ireland) one-way ticket from Paris (France) to Berlin (Germany) would be counted in Ireland's GDP.
Conceptually, an export is any good or service sold by residents to non-residents. So, if the above one-way ticket were purchased by an Irish resident, then it should be counted as consumption in Ireland's GDP. If it were instead purchased by an Irish non-resident, then it should instead be counted as exports in Ireland's GDP. (I don't know though if in practice they actually make this distinction.)
*In practice, I am not sure how exactly this is done by national statistical agencies. My suspicion is that they probably don't consider each ticket sold and instead just look at aggregate figures provided by domestic airlines, e.g. their profits.