This seems to be very odd if changing your format solves the problem. I would still create a new column with MMMM format and use your integer month column for sorting by. Just click on a new MMMM and change sort by option.
Can you also show, which fields you use and how in the visual? If you want to see the outcome as you have on lowest picture, you need to do following: 1. Put values in Y axis 2. Put Months in X axis 3. Put Year in Legend.
This should work fine.
If my answer was helpful please give me a Kudos or even accept as a Solution.