This could be anything from a mild irritation by an airborne irritant (like dust, pollen, their own feather dust) to a sinus infection.
In the case of infection, they usually end up with a residual discharge on their nares (runny nose) that is thick and white or yellow in color.
If it is just irritation from an irritant, there should be no discharge on the nostrils or in them.
If it gets worse, I would see an avian vet for a look-see and a bacterial/fungal culture.
You might just try getting a HEPA filter to run in the room. Often, their own dust builds up in the air and can be a source of chronic irritaion.
The behavior of imitating your sneezing is possible - I have an Amazon that is uncanny in her ability to sound like my sneeze, but I would only decide this after a little investigation to rule out infection.