I had a similar issue with my Surface Pro 3, when connected to a docking station, using the same StarTech MiniDP splitter. What eventually fixed my issue was this:
- Download video drivers from Intel
- Manually install the drivers (not using the .exe installer, but going through Device manager and using the option to Update Driver > install drivers manually > let me pick from a list... > Have Disk... > then point to the folder with the downloaded/unzipped drivers)
- Use the Intel Graphics Control Panel > Display > Multiple Displays to identify and configure the display arrangement.
Known issues:
Windows 10 updated itself at some point and "updated" my working Intel video driver with one that no longer worked. I had to repeat the process to get my setup working again.
Sometimes, when docking and undocking my device (disconnecting and reconnecting the displays) I still have to repeat step 3 above to make the displays recognize.