It is possible that your different computers are assigning differing drive letters to your external drive (also ref: http://forums.thebrain.com/tool/post/thebrain/vpost?id=2372273). I don't use fruit, but on windows you can force the external drive letter with the following steps: No idea if this solves your issue but worth a try.
Open Computer Management application
Go to Storage and click on Disk Management in the left hand panel
You should see your drives listed in the right hand panel
Right click on your external drive and click 'Change Drive Letter and Paths...'
and then choose a path letter that matches the drive letter as it appears on your mac or also force the drive letter on the mac side as appropriate
TB8022 32bit Java 32bit Version 8 Update 141 Firefox, Office 2013 Pro Plus 32bit 64bit Win10Pro 64bit Primary Laptop, 8GB RAM, Intel Core i7 64bit Secondary Laptop, 64GB RAM, Intel Xeon E3 Brain user since zygote