Actually IPP API is pretty much consistant with the rules defined for it. It might be different from other SDKs you tried.
Did you look at IPP sample package, we have several samples which can be built on Windows, Linux and Mac OS. This may help you to find where is your problem.
The comment from our expert is:
1. You do not need to care on normalization for a0, it is done at initialization stage by ippsIIRInit function
2. first order filter is equivalent to multipication on constant and was not specifically optimized (you can use ippsMulC function)