Pronouncing pinyin "c" in Shanxi dialect
Your pronunciation is correct. 

This is a common mis-pronunciation in many places in China, not just Shanxi. In fact, this is so common that nearly every modern Chinese input software supports so called "模糊音"（ambiguous pronunciation). The user can config if this function is enabled. Here's a screenshot of the config in Google Pinyin software:

 

As you can see, there are more than just "c" and "ch".

This is actually also a problem in China. It's a common topic in the many exams of Chinese language. The national exam for entrance to university used to have questions on this every year.