Minecraft – Playing Minecraft with a controller, except the controls are all wrong

If it looks OK in the windows game controller control panel, Joy2Key is the issue.

Try using xPadder instead, it is far superior to Joy2Key. There is a free version linked in this question: How can I emulate keyboard and mouse commands with a game controller?

Also if it's this adapter, it says something about changig the function of the stick by holding start and A for 3 seconds: http://www.mayflash.com/Products/PCUSB/PC051.html

I pulled this from an old stack question, I would suggest doing a hard reset on the controller. I know the symptoms don't line up exactly but if its a firmware or software issue it should resolve the problem.

If your controller won't pair, won't respond, or is displaying a flashing light, please follow the instructions on how to reset the controller:

1. Turn off the PlayStation 4.
2. Locate the small reset button on the back of the DualShock 4 near the L2 shoulder button.
3. Use a small, unfolded paper-clip or something similar to push the button (the button is inside a tiny hole). Hold the button down for a couple of seconds and release.
4. After resetting the controller, re-pair the controller with the PS4 by connecting the USB cable to the controller and the system, and turn the PS4 on.
5. Press the PS button to log in to the PS4

If this doesn't work, then you have a hardware issue on your hands and should look into cleaning your controller.