I have a Behringer UMC1820 plus ADA8200 for 16 Midas mic pres, and they both work fine in Linux.
Once you select ALSA as the audio system for REAPER to use, you also need to click the down arrow buttons on Input and Output device then select your UMC1820 on each so it looks like this, with the exception that you might need more than 64 samples buffer, depending on how fast your computer is.