Even test pilots are not always hired directly by Airbus, but most of them. (Also engineers are partly hired via third party companies, that's part of their employment politics.) Of course it "feels" as if you are working for Airbus, but in your contract is stated another employer.
The shuttle crews are not Airbus employees, since Airbus does not operate the shuttles itself (operated by PrivatAir or OLT or WDL on behalf of Airbus). The airplanes even are not entirely Airbusses, also BAe-146 and Saab 2000, because obviously Airbus does not build planes that size.
The Beluga crews are all former French military pilots with one exception (known to me).
I dunno much (if anything) about the training pilots, but can imagine that personnel of training facilities are also partly subcontracted.
Sorry, that doesn't make things easier, I know.