What ever happen using MG3700A but Siglent SSA3000X is extremely critical about external reference signal. Of course it need be stable and accurate enough but also it need be clean, as clean as SSA need reference clock. It also is very sensitive for ExtRef amplitude modulation. Just: All need be clean.
Some other machine may work so that it only follow ext ref carrier.
It looks somehow like that Siglent perhaps totally swap whole reference, internal or just external. And if this is case, dirty reference makes all results dirty. Just like garbage in - garbage out.
Here is three images one is not necessary but for better visibility.
Image 1.
100MHz CW from 30 years old HP Rf generator. In this image Siglent run with its own internal reference. (same as in image 3 trace D but other shot)
Image 2.
Signal used as External Reference for SSA in Image 3.
10MHz carrier AM modulated with 35Hz and modualtion depth 1% (35Hz sidebands -46dBc).
Also this same signal is used with 10% modulation depth (35Hz sidebands -26dBc)
Image 3.
Trace D: as also in image 1. (SSA using internal reference)
Traces A and B: SSA use ExtRef as image 2.
Also after done other many tests and my conclusion (until other real evidences) is that
do not use SSA ExtRef until you have high quality very clean reference signal for this purpose.