Open DOSBox config, find joystick section, find entry that reads "timed=" If it's "true", change to false, if it's false change to true. I don't remember the default value, just make it different. Start the game with the stick plugged it and see if there's any change.
The joystick+dosbox issue is that by default calibration is set up to work at a particular CPU rate. When cycles are on auto or max, cycles can change as the load changes: calibaration screen, menus, in-game, intro - all get different speed and different stick input. When you flick the "timed" setting, the stick becomes stable.
Thanks for the clue, worked for me. I didn't had a joystick section, so I created one in dosboxT2K.conf :
then I could perfectly play with my xbox controller.
Also thanks to RiffRaff1138.
I didn't have a [joystick] section either, tried making one on the same line using the format used by the rest of the file (no spaces), didn't work. Skipped down a line and pasted it in using that format (each bit on it's own line), worked perfectly. Just posting to confirm in case anyone else has trouble.
Also, glad I was able to find the solution here, just beat episode 1 (using a wired xbox360 controller :D) and am loving the game so far. Thanks a ton.