BB cable guide - where does the plastic tube go?

I have a puzzle that I'm hoping the road.cc brain trust can help me resolve.

In the process of replacing the bearings on my wife's 2012 alloy Cannondale Synapse, I managed to dislodge and break the gear cable guide under the bottom bracket. So I'm having to replace it.

It's a press-in fitting - not screw-in. I've bodged a temporary solution which relies on cable tension to keep the fitting in place, but I seem to have significantly increased the friction on the cable run in the process.

I'm wondering whether I have incorrectly fitted the  ~10cm long plastic tube  around the front gear cable as it runs vertically from the cable guide to the front mech.

So what is the purpose of this cable?

Is it intended (a) to be a low friction liner for the cable guide, in which case it should run *inside* the BB cable guide, or (b) to help keep dirt off the cable in that area, in which case it should propably remain *outside* the cable guide in that area of the bike, or (c) something different.