Welcome, Jake, to the OEM forum.
What you might be seeing is the inherent inaccuracy of a current transformer at low currents. What you have there is a 100 A device that’s specified to have a 3% linearity between 10% and 120% of the rated current. In other words, the manufacturer won’t even give a value for the accuracy below 10 A. However, when I’ve measured a SCT-013-000, the output goes well below 9 A still with reasonable accuracy, so although you’ve given no details of how the readings don’t match up, I’d suspect the layout of your input circuit might be picking up noise, and you are in fact measuring electrical noise - possibly from the power supply you’re using - as well as the voltage across your burden resistor - which at 10 A primary current is 165 mV.
What you can do to improve the accuracy is use a multi-turn primary winding - pass the wire through the c.t. a number of times, up to 7 - and then divide the current reading by the number of turns through the c.t.
Be mindful that 7 turns carrying 13 A bunched together can get warm, so you should consider using thicker wire (possibly up to 2.5 mm²).