Hey Cosmos,
I have a few question to try and help you out. I've actually been testing on a Mac with a PS4 controller mostly so there might be a problem.
Are you on PC or Mac?
Did you connect the second controller for the first time after the game was open?
Were you at the base?
Does the second controller work with other games?
Did you try pressing A on the xbox 360 controller?
Can you try joining player 1 with the controller then pressing space on the keyboard to join in second player with the Keyboard/Mouse and let me know if both work?
Thanks for the feedback. Hope I can fix this quick if there is a problem,
Rafi