IntelliJ IDEA Terminal brings his own colors from System?

It probably happened because you had customised your cmd.exe default colors. Resetting them back to default white text on black background fixed it for me under Idea too.

For immediate effect, you can try using color 07 command in terminal to set it to white text on black.

None of the other answers quite worked for me.

What did work is this:

(in Settings -> Tools -> Terminal -> Shell path)

"cmd.exe" /k color 07