There are many aspects of dissociative identity disorder that fly in the face of 'reality testing', that do not and should not warrant a diagnosis of psychosis.

Examples:

A child alter in an adult body
A male alter in a female body
A female alter in a male body
An animal alter in ....
An age-slider alter
An introject alter
An alter who is 'stuck' in a previous traumatic event
An alter who denies being the original person (ie: pretty much every alter that exists!)
etc etc etc

All of these are examples of believing something that is not aligned with actual reality, in the context of DID. And what about these scenarios:

Alters having conversations within ones mind (co-consciousness)
Alters deleting thoughts, adding thoughts, or otherwise manipulating the experience of the presenting alter
Alters creating an internal safe place

Do these things exist in the external reality? No. Is that then evidence of psychosis? No. No it is not.

The reality testing of every single person with DID is impaired. But that does not equal psychosis. (It doesn't rule it out as a dual diagnosis either, but that is a different story).