can you describe "TFSF"? From your gif, there is obviously reflections at outer most boundaries and you also introduced a inner boundary that reflect field as well. You said you did not put ABC, PEC, PML, but obviously you have two boundaries at outside and middle. You are contradicting your own statement.
For a 2D FDTD, I always start with pure 2D problem, one cell along z direction with top and bottom set as PEC. Then the XY walls set as ABC. In such case, you should see the wave excited from the center should propagate out as a pure circle, and get some reflections at the XY corners due to the 1st order ABC's poor performance. If you can see this, it means your 2D FDTD should be in principle working.