I am the developer of Tricone Lab which you linked above.
I guess the first thing to say about the Tricone Lab topology layout implementation (i.e. dynamically adjusting curves) is that it does not use any off-the-shelf physics engine like Box2D. It uses a very specialized library which I wrote myself for dynamically updating 2D planar graphs.
My library uses a data structure which maintains topological relationships. So we have a set of regions, edges and nodes, but we also always know which regions border which edges, etc.
Each edge is made up of a list of vertices but this list can grow or shrink. Each region has a target size (i.e. area). If a region is below target size, then a "force" is applied to the normals of the vertices of the edges bounding the region. Forces are also applied to smooth out edges, to prevent nodes and edges getting to close to each other, and to prevent anything getting too close to the edge of the play area. The combination of different forces on each vertex is summed at each timestep and the vertex is moved according to the balance of forces. An edge acquires a vertex between a pair of its existing vertices which are too far apart (above some threshold). Similarly a vertex is deleted if it is too close to its neighbour.
So that's more or less how the "physics" works. It's probably not something which you would want to apply in another game, unless that game is also about 2D planar graphs.
However something that you might be able to take into your game is the idea that a curved edge has a variable number of vertices which adjusts according to the conditions, so that vertices are added and deleted dynamically to maintain smoothness.