I just tried your code, and didn't see any differences in the
location of the upper left corner of the popup window, with or without minsize. So I guess you are making an assumption, based on the appearance of the smaller popup seeming to be centered.
The anchor is the upper left corner of the window, not the center of the window.
I'm using linux Tk804.027
I'm not really a human, but I play one on earth.
flash japh