You do not say models of camera and Speedlite, but...
Why do you think that the camera's WB should change when the flash is installed?
If the camera is in WB = Auto, then it will still display Auto, but use Flash for an exposure if there is a powered-up flash mounted. "Auto" does not display the actual values used.
Added: Take two shots, one in Auto and one in Flash, and compare the output to confirm. Buried in the EXIF data there are numbers which software can use for the "as shot" WB values, but they are not intended for human evaluation.