Hi Kevin,
We do not have the iStar Pulsar or Fusion cameras in our database at the moment. However, the good news is that for spherical cameras, focal length and distortion values for the camera model are not required, so you should be able to use them with the software even if the models are not in our database. The necessary information should be stored in the EXIF tags of the images.
Note that, for spherical cameras, Pix4Dmapper only supports the equirectangular image format. Learn more in What is the equirectangular Image format?.
I hope other users can share their experience using such cameras with you!