See the online U3821DW User's Guide, page 42. It explains the Input Source- Auto Select for USB-C options = Allows you to set Auto Select for USB-C to: Prompt for Multiple Inputs: Always displays the “Switch to USB-C Video Input” message for you to choose whether to switch or not. Yes: Always switches to USB-C video input (without asking) when the USB Type-C cable is connected. No: Never automatically switches to USB-C video input when the USB Type-C cable is connected.
I have a U3821DW (LOVE IT!) with my work laptop connected via USB-C and my personal desktop connected via DP. As long as it's plugged in, the laptop seems to always be primary. I don't recall setting it this way, but it's annoying to sit down and want to use my desktop and have to first log into my work system and then hotkey to change over (the buttons on the back of the monitor are hard to reach for me and really not the best, honestly). Is there any way to make my desktop primary? It's also too easy to get into work by going through that system first. I looked and did the requisite googling and can't find a way but I figured maybe someone did! DDM and monitor firmware are up to date. 
U3821DW, changing primary monitor