[@Achronum]
In answer to your question
[b]When in a shadow field[/b];
The reality is the same, but shadows and can appear at until defeated, both the shadows and cosmic princes are invisible to civilians. 
(Unless a civilian is pulled into the field, if they are safety reduced and released, they will have no memory of the events)
When the cosmic princes are transformed, their identity is shrouded in mystery, no matter how little they change when transformed.

[b]When outside[/b];
Yes, but their identity would be shrouded, it is assumed that all fights would be taken in a distortion field. Or in a seriously isolated environment.