Unexpected result after calculating the response of a system in frequency domain
That's not strange – that's expected! 

The DFT is a circular operation – by shifting to the right, your signal "wrapped" around.

What you need to do is called fast convolution based on the DFT/FFT. The Wikipedia has a nice article on the Overlap-Add and the Overlap-Save methods, so I'd recommend starting with these, and then going for the literature that suits your understanding best.