Assuming you chose Fluorescent WB becuase the lighting was fluorescent, then yes, it's normal. It's because of the fluorescent lighting, and it's not a WB issue. Basically, fluorescent light actually flickers - faster than your eye/brain can perceive, but not faster than a camera's shutter can be set. The flicker is timed to the alternating current of the power source. If your shutter speed is at the cycle frequency or slower, you're fine. If your at twice the cycle frequency, you're usually ok. In between 1x and 2x, and faster than 2x, you'll get irregular color, and when you get faster than the camera's max Xsync speed (the fastest speed at which the entire sensor is uncovered during imaging), you'll also get uneven illumination.
In the USA/Canada, AC power is 60 Hz, so 1/60 s and slower is fine, 1/125 s is usually ok. Your shots are at 1/125 s, so I'm guessing you're in a part of the world where the AC power is 50 Hz. Try 1/100 s, or 1/50 s or slower, or overpower the ambient lighting with flash.
