Is there any software in addition to Avant that is running on all four computers?
I don't get tooltips at all on anything (menu items, buttons, icons) in the top row in Compact Style or for anything in the menu bar when Compact Style is disabled. However, I noticed that if you disable the Management Bar, the small down arrow that's normally at its left end and any buttons you have enabled in Other Buttons (except for the first five, which appear in the Search Bar) appear inline with the menu bar either just below the title bar in regular mode or in the title bar to the right of the menu in Compact Style. I have all the buttons that normally appear in the Management Bar disabled, and I have disabled the Management Bar itself, so the small down arrow from the Management bar appears to the right of the menu. When you click this down arrow, you get a menu of several commands, and below that, a list of all your open tabs in reverse order with the PID included. When you hover your mouse cursor over any of the tabs in the list, you get a tooltip that shows the entire tab title, including the portion that is cut off at the right end in the list. I'm thinking that these tooltips for the tabs in the list may be what's showing up in your case. I don't know why it's happening, but it's a more likely explanation than anything else I can think of, and maybe it will help to determine why you're getting those tooltips.