Dolby Atmos is 3D object oriented format: it takes a fixed number of channels and objects to simulate a 3D space, and then map that to whatever speakers/headphone you have. In order to use Atmos, you need both the speaker setup, the material, and a system that has the decoder.
Consumer Atmos tracks for home movies have a meta-data stream (Joint Object Coder) that has up to 16 dynamic channels (channels or objects for tracking), then also a fixed surround stream (that’s either static 5.1 or 7.1). If you stream a movie in Atmos, the static stream is 5.1 Dolby Digital Plus (and if your system doesn’t support Atmos, it will see it as a Dolby Digital Plus track). If you’re watching a UHD disc, the static stream is 7.1 TrueHD (that a non-Atmos system sees as TrueHD. Apple Music now has some songs in Atmos (since their headphones use Atmos for their 3D rendering. The surround stream Apple uses for lossless is their ALAC (so Atmos JOC stream is within that track).
For a headphone system, if it doesn’t have the Atmos decoder in the mix, then it would just be seeing the 5.1/7.1 surround. And it would be applying its own process for binaural overhead effects.