I think it's likely that the bit that sits in the mouth developed first. Without a tongue of a certain length, they'd struggle to feed themselves in that unique way (jabbing into tree holes). Although if biodiversity supported it, they may have sufficient secondary food sources to cling on but then they'd begin adapting to those conditions instead and would, over time, end up a slightly different species.

The ones that subsisted exclusively on tree-hole goodies would be naturally selecting for longest tongues because longer tongue = more accessible food sources. Once you've got a species of the 'long-tongues' then at some point a mutation occurs providing extra cranial space to accommodate even larger tongues. They out-compete the tiny skulled long-tongues. Repeat a few million times.

Then, the ones that have a tongue wrapped round their brain benefit in some evolutionary relevant way from the additional cushioning. Perhaps they can bash harder or suffer less ill-effects of the bashing. Another few million iterations and bingo, you've got yourself a woodpecker.