I also see this problem in 4.13.0, the latest version as of this reply.
The entire particle system is attached to a bone and the ribbon trails are attached to source particles. The instant it breaks is when the source particles are set to local space to move with the bone. When this happens, the ribbon trails get offset a short distance away. The ribbon trails look correct when the source particles do not move with the bone.
There are no offsets in the required module of the ribbon emitter. There are no orbit modules on either the source or the ribbon emitter.
Possibly already reported as UE-22714 but I’m not sure if it’s the same issue since I am unwilling to jump through all the hoops necessary to find out.