Often editors keep track of the overstrike/insert mode that was in effect when you edit a particular file. When you change it afterwards in a different program, the editor may set it back how it was last time you used the editor or even edited the current file. Usually there';s a different cursor depending on which mode is set. Are you getting overstrike when the insert cursor is showing? That would be strange for sure. I don't remember seeing anything like that. At least not for some time.
What editor or program are you using when you get this?