The only tilings with rhombic lattices are those of type cm and cmm.
The reflection axes (dotted lines below) for these tilings are not in the same direction as rhombus' edges (the solid lines).
For this reason (although for all I know there may be others), centered cells are chosen for tilings with symmetry groups cm and cmm. To get a centered cell, draw a rectangle with lattice points at the vertices and a lattice point at the center.
A centered cell has twice the area of a primitive cell
Tiling Definitions Identifying the 17 Plane Symmetry groups