What are the geological mechanisms for sea floor spreading in the Bismarck Sea?
Ah yes, this is a very good question. The formation of back-arc spreading centers is an open research problem, and happens to be the main topic of my office mate's dissertation! While these aren't exactly "clean" back-arcs, the formation of them is similar, I'm fairly sure. 

The formation of back-arcs is caused by "Trench Roll-back". Trench Rollback is where the trench is pushed back in the opposite direction of the subducting slab and causes extension in the back-arc, forming a spreading center.  Below is a diagram from Modeling the dynamics of Subducting Slabs, Magali Billen, Annual Reviews of Earth and Planetary Sciences, 2008:



You can ignore the "Shallow" vs "Deep and Wide Box" comparisons, those only matter for building a modeling domain. What is important is noticing what happens to the slab when it hits the 660km boundary: it has a much more difficult time subducting. The slab "glides" through the upper mantle, but deeper in the earth, the mineralogical phase changes make the mantle much denser, creating a much stronger normal force on the slab. This normal force transfers energy into the slab and "pushes" back causing a drag between the deeper slab and the slab in the upper mantle. Since the under-riding plate and the overriding plate are weakly coupled viscously, only a small portion of the overriding plate is pulled with the trench. This causes extension/rifting. 

Not all subduction zones have a back arc: weaker slabs tend to have a much harder time forming one as the transfer of energy in a strong slab is much more efficient. 

It is also important to note that these phase changes are currently the leading theory, but our dynamic models have a hard time dynamically developing trench rollback. Sure, the literature might sound optimistic about it, but thats with surface kinematic boundary conditions and not pure dynamics. 

These rifting centers form from trench roll-back. We can measure this roll-back with GPS. What causes trench roll-back is a much harder question to answer, in my opinion.