Not sure about your setup. Your "signal conditioner" is actually a charge amplifier. Are you using it as intended?
Also, are you sure of the output of both the func gen you used and the Extech signal gen? Have you measured both with a good voltmeter?
In your first test, you get an amplification of x102 actually, which is +2% error. Way above the +/-0.5% noted in the signal conditioner's specs. So either your signal generators are the culprit, or you are actually using the signal conditioner incorrectly, which I suspect. As far as I've understood, it has two modes (charge input or IEPE), which are you using? Is it adjustable? In IEPE mode, I think the inputs will be sourced or sunk with a 4mA current (meant for sensors), so that could very well disturb the output stage of your signal generators. This may be adjustable, perhaps you have it set all well, but I don't know. This signal conditioner is not just a voltage amplifier.