When Proportional Edit (Connected) is active, the same translation of a vertex in 3D View doesn't equal UV / Image Editor's translation of the same vertex.
UV / Image Editor doesn't take distance by edge into account (only checks if it's an island).
Both movements should be like seen in 3D View.
Exact steps for others to reproduce the error
- Open the File
- Try to move the selected vertex in both 3D View and then in UV / Image Editor