Yep, any power coming in over-driving you main mixer will result in a bunch of spurs, even if it's off screen. Most HP analysers I've seen like the mixer to run at -10 dBm, so set your attenuation to bring your input signal below -10 and try again.
To make it clear to a beginner, that is -10dBm at the
mixer's input, not the instrument's input.
We've had engineers come in "guys the transmitter has a ton of noise all over the GPS band!" when they were feeding the SA 15dBm from a coupler but had the SA at the minimum 6dB attenuation when they were looking at the GPS band. A filter to kill the carrier convinced them that it was just poor measurement technique.
As with any measurement, but especially with RF instruments, it is worthwhile playing around with the controls to see what happens. If you expect what you see, great; if not then also great - because you will learn something.
The most excitign sound in science isn't "Eureka!", but "That's odd..."