I play on both Xbox One and 360 due to friends of mine having not yet upgraded.
Having purchased the DLC on the xbox one (mainly due to the ease of use of the app) it appears I am unable to use the DLC content (EV-30 Tumbler) on any of my characters on my Xbox 360.
I really would rather not pay £35 again for DLC on the 360 as well as having already paid for the Xbox One. Especially as us xbox users are not getting every bit of the developed game just yet anyway.
Hopefully somebody can shed light onto this matter.
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I'm afraid you did it backwards. The offer from Bungie is a digital upgrade path from the 360 to the One - not the other way around. I play on both consoles and just bought the dlc for the Expansion Pass for the 360. I then got the dlc for free for the One.