Perhaps at home you have your Finder preferences set to "Keep arranged by:" something, and at work you don't. I don't know why a rearranging would be specific to booting, unless it is determined by mount time or something on external drives.
From the desktop/FINDER
*Arrange Current Desktop
FINDER -> VIEW -> Arrange -> Size or Name
*Arrange For Current Destop, Active Changes, and Next Boot
FINDER -> VIEW -> Show View Options [Command]+[J]
Snap to Grid ? Your choice- Me No
Show Icon Preview? Keep arranged by? Select if you want- this can change the position of icons.
If you using a networked drive or removable drive, the local host stores the icon location, but the icon image (similar to a stack of PNGs) is stored on the host media. The same holds true for individual files, applications, etc... The exception to this rule are the default icons/bezels that are part of the OS. (Oh and locked media.) Some are easy to change , and others require some pay/shareware or access to root to "permanently" change them. Edit system resources and change permissions at your own risk.
I have no idea why I added this last bit, but it here if you want to change look of your media icons.