I have the previous model of those shifters, and there is no barrel adjuster in the right lever. Searching for the manual for this model, it has a section that says something like setting tension adjuster if fitted, which would indicate that one is not required. Also if you do an image search in Google, none of the right hand levers of this model have a barrel adjuster for the shifter.That can't be right. If you look carefully you can see that, as @raleighnut points out, the ferrule is pressing against a "castellated" or notched bed for a barrel adjuster identical to the one in the pic posted above by Dogtrousers. That bed (I can't think of a name for it) would be internally threaded for the barrel adjuster and thus not suitable for a plastic ferrule under considerable stress from the derailleur spring and cable friction, which explains why it has failed.
To the OP - was the shifting bad for some time before you spotted this problem?
As to the op's problem, possibly the tension in the inner was too high, maybe too short, and that caused the outer to fail. I think it needs a full new inner and outer, as well as ferrules.
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