Windows 10 Pro, 19043.1052
It was the latest downloaded version of Groupy (I uninstalled it). Not only were the original posted issues happening, but other weird blinking of windows was happening. Especially with Windows Explorer, if I had multiple Explorer windows open, I would hover over the pinned taskbar icon, select the window I wanted and it would blink. I would always have to then hover and open the first of the set of windows explorer windows to make all the tabbed windows show up appropriately and then I could click on any of the tabs. But if I basically selected (brought to forefront) any other Explorer window than the first opened, I'd get blinking.
It also wasn't playing nice with DisplayFusion's "Move to other monitor" title bar button. If I clicked the button and moved a tabbed window to another monitor, it would be a blinking mess, for a few seconds before settling down and stabilizing. I am not getting that behavior with TidyTabs.