I have been using Canon XH A1 since 2 years and I have been experiencing a very reddish look whenever the video is taken under low-lighting conditions especially if the lights are tungsten or any other source that emits light at the same degree of colour temperature, letting you to know that I always set the white balance function to automatic. This phenomenon is not very common if the lights under which the video recording is going on are florescent or any other source that emits light at the same degree of colour temperature.
Can anyone explain the reason behind this negative effect and how it can be resolved?

Pretty normal on plenty of equipment. Tungsten lighting is a very low colour temp (3000K for many lamps) - and auto white balance when levels are low is often biased to the reddy/orange colour - which of course is where the actual light sources tend to be. Manual white balance is pretty important when light is low, and once you get used to it, you can manage it pretty well - although even with tweaking in post, it's sometimes difficult to prevent the red hue overpowering some colours. You may well be able to get the whites white, but often the red colours are too red.