To be honest it's inconclusive. I usually treat Sabre as the oracle on this: https://www.sabre-roads.org.uk/wiki/B95_(Northern_Ireland) – and it initially states that the B95 begins from the A522 roundabout, but then points out, as already noted, that it is signed in brackets, which means the first stretch is not the B95, only a route to the start of it.

It might make sense for the section of Fountain Hill to be labelled B95 (and if so I would do it with both carriageways rather than one). But at the same time, there are instances of slightly nonsensical starts/ends of referenced roads across GB and NI, and the general approach is to map only what is there.

So, a sitting on the fence answer I'm afraid!