This is not a good dock for this machine. Machine has all thunderbolt ports, something like WD19TBS or any other thunderbolt based  would be a great dock for your computer as it will directly use your Graphic hardware to produce better quality video as well perform better in load.    This dock is using display link technology like Dell's D6000 dock. Creates a virtual software based Graphic card in device manager to driver those dual 4k monitors. All in all not using your computer's processing power to the fullest    A fix that may make this dock work : You need to install Latest display link drivers in order for this dock to work on your XPS 13. 
I have a Kensington SD4780P docking station, which I use for work and which supports dual 4K screens, alongside USB, ethernet etc. Its worked fine for 6 months with my work HP laptop. However when I connect my personal Dell XPS 9310 to it I can use the ethernet and USB connected devices, but the displays don't work. I'm running Windows 11 and when I try to "detect other displays" it comes back as undetected. I've tried rebooting, checking for driver updates but no luck, so not sure what else to try. Any ideas?
XPS 9310 Dual Monitors not working