Enzyme inhibitor leads to higher turnover rate?
While it's difficult to know just what is going wrong in somebody else's laboratory, apparently paradoxical effects like these are unfortunately common in laboratory work.  Assuming that these are indeed well-established inhibitors that really should be working, let's consider why they might not be in your hands.
The mechanisms of molecular interaction are complex enough that there are many cases where a substance that acts as an activator in one condition can act as an inhibitor in another condition. Another way that you could see such an effect is if your purified system is not actually as good as you think and the problem is being partially relieved by one of the inhibitors, e.g., imperfectly purified and addition of the inhibitor neutralizes some of the imperfections.
Not knowing the details of the compounds you are working with, it is not possible to guess which of the possibilities might be at work. I would suggest, however, that you begin by:

Comparing your quantitative turnover rate with the purified enzyme to the predicted rate from the literature to see if your baseline system is actually working correctly.
Make sure your system is also (not) processing substrate at the appropriate low rate when the enzyme is absent.
Checking for potential differences between your method and the method that you are trying to adapt from the literature, which might give clues to the condition differences that may be impacting your results.