Yes that looks to be correct in this case (although this strip board looks to be a custom part to do that, the standard strip board won’t do this). There aren’t actually two layers in the drawing, a wire connected to the B strip in breadboard will be the same as a wire connected to an A strip, the different color of the trace is the only difference that makes it appear to be two layers, Fritzing only recognizes one layer in breadboard. Perhaps I misunderstand what you want to do, but in breadboard you can only look down from the top of the board (I had assumed you wanted to flip the board so you are looking at the bottom side which Fritzing won’t do.) The board above appears to have been created as a custom part with a different color used for the bottom layer on one strip. It isn’t clear to me why you would want to do this because you can’t see or connect to the bottom pads (assuming they are there) under the IC. Wires (in breadboard) will only connect on the top of the board like this:
You can’t run the wires under the chip or flip the board to see the wires on the bottom side of the board or have a different wire connect to the bottom of a board (Fritzing will connect it to the top layer, the only layer it recognizes).