Throughout the game you will see on-screen tips telling you what you need to do with the controls to get past or interact something in the game. This will show up on the screen as "Press SPACE to [do something]". However, when using an Xbox One controller (and possibly even other gamepads) these tips don't change to reflect the input device. They still show tips for the keyboard.

While this guide will show you how to make this situation better, it still doesn't show the actual button to press, and instead displays the button name, like, "Press the Y Button to [do something]". It also doesn't cover how to replace the [esc] key with the Start Button, but this is such a low impact button that I thought that I'd write this up with the rest, since they are more useful to see on screen anyhow.

As it turns out, it's actually a really simple process, but it's not very intuitive to figure out. To start changing things around do the following:

1. Go into Controller Configuration.
   
2. Press the A button on Controller Configuration, which will take you down to the mapping section down below.
   
3. By default it shows the commands as KEYBOARD/GAMEPAD. What we need to do is swap those.
   
4. Press the A button on the one that you want to change, for example: JUMP.
   
5. Press the keyboard command that is already associated with this item. By default JUMP is the SPACE key so press SPACE.
   
6. Now the JUMP command should show as "A Button/SPACE" instead of "SPACE/A Button".
   
7. Continue to do this for the rest of the input items in the list that have an associated gamepad command.

Return to the game and you should see the changes immediately. If you happened to have a tip up when you went in and made changes, move away from the tip and come back to it and it should show the updated command.

From what I can tell, the game seems to display the left-most control in the command list, and all we're doing here is swapping the items in that list around. So now when the game has a tip to do something, like jump, you'll see "Press the A Button to jump" instead of "Press SPACE to jump". While this isn't the best example, there are some other commands & combos later on where the tip is a great reminder of which buttons you need to hit.

NOTE
As mentioned earlier, the only command that I haven't figured out is the ESC key. It's worth mentioning that this also doesn't change the displayed commands for navigating the menu system, so it still says things like "Press the ENTER key", but the menu follows the standard A=Enter, B=Back flow, so if you've played another game with a gamepad then you'll know what's up.

Hope this helps, and good luck!