XPS 13 9370, WD19 second UHD monitor limited to 2048x1080

@three-m  here's the short answer: You need to return the WD19 and get a WD19TB instead.  Then you'll be able to run dual 4K displays just fine.

Here's the long answer:
The D6000 worked because it uses DisplayLink technology rather than tapping into native GPU outputs.  Whereas most docks have the GPU directly driving attached displays, DisplayLink uses "indirect display" technology where the CPU and GPU compress video data and then transmit it as regular USB data to a chip in the dock.  That allows you to use more and/or higher resolution displays than would otherwise be possible because you don't have to worry about native video signal bandwidth or even the maximum number of displays supported by the GPU, but DisplayLink comes with a lot of drawbacks.  I wrote in detail about those in this thread, specifically the post marked as the answer.

The WD19 doesn't use DisplayLink.  It taps into the native GPU output wired to the USB-C port.  If you take a look at the WD19's documentation here, specifically the Display Resolution Table beginning on Page 17, you'll find that when the regular WD19 (non-TB version) is used with a system that only supports HBR2 over USB-C, aka DisplayPort 1.2 over USB-C -- like the XPS 13 models up through the 9380 -- you can only run dual displays up to 1080p (technically dual 1920x1200 works too) or a single 4K display but only at 30 Hz rather than the standard 60 Hz.  So you'll probably find that even your display currently running at its native resolution is only running at 30 Hz, which for most people is an unacceptably low refresh rate because it creates very perceptible lag even with things like the mouse cursor.  And even if your system supported the newer HBR3 standard, aka DisplayPort 1.3+ over USB-C, you'd still only get a single 4K display at 60 Hz or two at 30 Hz.  But as of this writing, there aren't any Intel GPUs on the market that support HBR3 over USB-C.  That won't be arriving until the Gen 11 GPU that will debut first with the Ice Lake CPUs, slated to arrive at the end of 2019 beginning with the types of CPUs that would be used in systems like the XPS 13.

However, since the XPS 13 models have Thunderbolt 3, you can return the WD19 and get a WD19TB instead, which takes advantage of Thunderbolt 3 and gives that dock access to 4x more display bandwidth than the regular WD19.  The WD19TB can run dual 4K displays each at 60 Hz even from a system that only supports HBR2 over USB-C.  I wrote a detailed post about the various operating modes of USB-C and Thunderbolt 3, and their impact on display configuration options here if you're curious.

And just fyi, the WD19's product page here only mentions support for dual FHD (1920x1080) or single QHD (2560x1440).  4K support isn't even mentioned because as I said above, even if you were only trying to run one of them, you'd only get 30 Hz rather than the normal 60 Hz, which most people wouldn't accept.  What even led you to the regular WD19 given that you have dual 4K displays?