MacOS – A small window opens for a seccond

There's two things I would try initially: testing your Mac in Safe Mode and, if that doesn't resolve things, resetting the NVRAM.

Test your Mac in Safe Mode

Follow these steps:

1. Fully shut down your Mac
2. Restart your Mac
3. Immediately press the Shift key and keep it down
4. Let go of the Shift key when you see the login window (NOTE: If you have FileVault enabled you may need to log in twice).
5. Take a note of what happens (i.e. test your keyboard entry as per your question)
6. Exit Safe Mode by restarting your Mac as normal
7. Test again to see if the problem still persists

If the problem still persists after following the above steps, you can also try resetting the NVRAM.

Resetting the NVRAM

Older Macs had what's called Parameter RAM (PRAM), newer Macs use Non-Volatile Random-Access Memory (NVRAM). Since you haven't specified the exact model of Mac you have, follow these generic steps to reset the NVRAM:

1. Shut down your machine. Yes, a full shut down, not just logging out.
2. Press the power button and then immediately press the commandoptionpr keys.
3. Keep these keys pressed down for at least 20 seconds!
4. Let go of the keys and let your Mac reboot normally.

Note: When you log back in you may need to readjust some of your system preferences (e.g. speaker volume, screen resolution, startup disk selection, time zone information, etc).

Let me know how you go.

According to macOS, windows should not be behind the Dock. When the bounds of a window are updated, macOS moves any windows from behind the Dock above the Dock.

The window bounds update when you add a new tab, so macOS looks at those bounds and moves them such that they don't overlap with the Dock section of the screen. There's no way to change this currently.

As for why this happens in High Sierra and not in Sierra, I presume it's because Terminal now uses the unified tabs functionality provided in AppKit.

Terminal has always had tabs, but macOS recently introduced tabs as part of the OS, for any app to use. I believe Terminal now uses this functionality for its tabs, which has caused this. You can test this by opening Terminal with multiple tabs and pressing ⇧⌘\ for Show All Tabs — this is functionality provided system-wide by the OS, not by Terminal, for managing tabs including the tab bar.