No, that's not normal for a microscope. Once you have it dialed in, you see one image, not two circles.
have the rubber eyecups slightly resting on the bridge of my nose
I have an Amscope and I wear glasses. If you have a really big nose and narrow interpupilary distance, you might have a similar problem.
Try taking off the rubber protective rims from the eyepieces. With glasses on, I am not able to get close enough to the eyepiece. That fraction of an inch makes a huge difference. If your nose is touching the rubber rims, maybe you are having a similar problem.
That said, for the life of me I can't figure out how the bridge of your nose could be resting on the rubber rims. Does your face look like Josh Rosen's by any chance?
The eyepieces adjust in width. I know that sounds obvious, but I know a guy that never figured this out on his own and couldn't use a stereomicroscope until I showed him. i am a bit dubious that you have them set, properly. It sounds like they are too close together. Else you have a spectacular nose.
**All that said, i wonder. The distance between eyepieces can be adjusted, but the angle? I wonder if the angle remains the same. So that someone with a larger PD (interPupillary Distance, in optometry speak) will end up aiming their eyes "farther out." and someone with with a small PD will have to cross their eyes more.
My PD is on the larger side of average. My experience is that the image appears close to me, but my eyes have to do a "100 yard stare" kind of thing, which is disconcordant with how close the image appears. And immediately after using the microscope for a spell I find it taxing to focus on things that are up close for awhile. My eyes don't want to cross so much, anymore, to converge on things that are only a couple feet away. I wonder if this experience is lesser or even reversed for someone with a short PD.