Any X11 application that pops up a window, albeit a tiny window like the hints tooltips, will make Spaces switch desktop spaces. Nedit also can do this. Even other native Mac Cocoa applications can trigger a switch of Spaces by opening a pop-up window at timed intervals. Under the most recent versions of Apple updates and Xquartz, the behavior seems to be that the Space will will switch back to the X11 application (afni, nedit,?) if in a different space.

Otherwise, if on the same space, the applications will show the X11 tooltip through a native Mac application. I've attached a screen capture of the tooltip in Nedit. This is an old problem though with X11 on a Mac and not very dramatic compared to the Space switching.

I've been communicating with Apple reps about this, and this has been reported several times to them. There might be a fix for this in the future. In the meantime, you can do any of the following:

1. Avoid Tooltips in applications (for AFNI, set AFNI_HINTS = NO)
2. Don't use Spaces
3. Use shareware Desktop Manager. This seems to work now with the latest updates for Leopard and Xquartz