It is best practice to insert a ZOH block after the input port to the model as it will convert an input signal with continuous sample time to an output signal with a discrete sample time.
The reason you are getting incorrect results is likely because the fixed point data type has not been selected correctly for your specific signal data range. If you use the Simulink Menu Bar -> Analysis -> Fixed Point Tool utility, this will simulate your model, derive signal ranges, and automatically propose data types that prevent over/underflow errors while maximizing resolution.
Finally, the blocks are colored red to indicate the particular sample time. This can be changed by clicking: Display -> Sample Time -> Off. Also, click Display -> Sample Time -> Display Sample Time Legend will pop-up a window describing the meaning of each color.
