Maybe it's because I subbed to this mod long after I had LVM's Deep Storage (DS) but anyway, this issue can be fixed by going into LVM's DS mod options and re-setting the "Deep Storage defaults to Storage Priorty" to "Important" or whatever you want it to be.

From there on every JDS crate should default to the set priority - mine was already at Important but re-setting it to Important seemed to do the trick.

Edit: This seems to be a re-occurring issue whenever I load up a save but can still be fixed the same way.