If you are using macOS 10.14.6+, you can accelerate applications with the external GPU (if they support GPU acceleration)...
Select the app in Finder
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Check Prefer External GPU
Adobe Premiere and Apple Final Cut Pro automatically use the eGPU when appropriate. Do not select Prefer External GPU for these applications.
Some professional applications let you select the external GPU (or multiple GPUs) in their preferences.
If you are connecting from a DVI (or sometimes DP) port on your GPU Card--via an adapter cable--to an HDMI port on your monitor and the display looks magenta, you can fix the issue in the monitor control panel. Go to the monitor Color Settings; select Input Color Format; change from RGB to YPbPr. That should solve the problem.