I believe the Filemaker Application on your Workstation is saving the most recent import field mapping order. Moving the file to the server leaves this info behind with your application. To preserve the field mapping, you should put this in a script with the Export records script step. You can use this to save/store your field mapping.
Note that there is a dangerous, long lived bug that you need to keep in mind when mapping import/export fields in Filemaker. See the following thread for a description and a lot of sound and fury towards FMP Inc.
Thanks for the tip. I'll read up on scripts. I've never used one in FM. Fortunately I'm just exporting, not importing, it looks like importing has the most detrimental effects on the database.