Trying to Sense When a Window Appears

Seems like you have answered your own question: The target window always appears just after the app is launched.

As @jonathonl suggested, we need more info:

  1. Name of app (with a link to its web site if not a common app)
  2. Can you close the window with a keystroke, like "ESC" or ⌘W?
  3. Please post a screenshot of the window.

When the target window is open, try running this to get more info about it:
EDIT: Remove that link. Looking for the correct link.

Please read:
Tip: How Do I Get The Best Answer in the Shortest Time?