Sounds like there's a issue with your projector or HDMI splitter. Your monitor and projector are both sourced from the same HDMI cable, so they should be identical. I'm not sure what would cause such a strange effect, you could start by checking cable connections.
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It's strange such a thing is even possible...
Does everything fade slowly on the projector?
For example, if you open a file browser on the projector, then close it, do you observe an afterimage?<br>