Prevent Apps from staying in dock

If you don't want to see the last three used app in your dock, go to System Preferences/Dock and disable the feature "Show last used apps in dock", and this section of the dock will be cleared.

Simply click and drag each icon from the Dock until Remove is shown.

▷ macOS User Guide. 

Once an icon is removed, it only shows up when the app is actively open, then disappears when the app is closed.

▷ macOS User Guide. 

Has the User ( you ) installed any Third Party Application that has or does Modify the Normal behaviours of the Dock ?

Has the User ( you ) used a Terminal Command to alter, modify or otherwise change the behaviours of the Dock ?

1 - Suggest restarting in Safe Mode. This will perform a Disk Repair, clear cache files and only load Apple Software, extensions and fonts. The boot up will be slow and can take some time - Normal.

2 - Does the issue present in this mode ?

3 - If not - there could be something in the main User Account playing up. To further isolate this - Set up users, guests, and groups on Mac. Then log out of the Main User account and log into the dummy account and test again if the issue persists.

4 - If the issue is present in the dummy account - then, this appears to be a System Wide issue on the computer.

5 - If the issue persists after attempting each of the points above and in that order - please advise for possible additional Trouble Shooting and possible solution(s)

Well, good you seem to have found a solution.

Bye the by, the Terminal command quoted is a form of a Tweak.

Have it resort to such measures maybe indicative of some other underlying issue not yet discovered by the User ( you )

Try it the other way, maybe it will stick: when that application is running, click and hold the Dock icon, choose Options and UNcheck the box for "Keep in Dock". Quit the application. Did it go away?