well, generally, the thermal noise floor at the input of the spectrum analyzer will get LOWER if you LOWER the step attenuator at the front end.
So if you are seeing the reverse of that, then something is odd about your signal, or your spurious outputs, that are overloading the spectrum analyzer somewhat, or some other artifact of the FFT that the baseband of the analyzer uses. this sort of thing happens a lot when measuring modulated signals, as the specific attenuator, rbw, and vbw settings determine how the signal is displayed
And as a separate comment, a spectrum analyzer front end is for all intents and purposes a mixer...so lowering the input step attenuator drives that mixer harder, and generates new spurs INSIDE of the spectrum analyzer itself. in other words, you can fool yourself to think there are more spurs, or higher spurs in your device if you have too low a step attenuator setting,