The problem seems to be that the minimum size is forced by the window manager, not by the Tk internals. So Tk only sees the requested size of the label and calculates the position according to this size. After (or while) the window gets mapped, the window manager forces the window to be larger according to minsize.

A fix could be to a) set explicitely the window size to the minimum and b) to not allow pack propagation before the window is mapped. Something like this, to be inserted before the Popup call:

$popup2->GeometryRequest(162,190);
$popup2->packPropagate(0);
[download]

After the Popup, you could turn pack propagation on again.