Thanks for the answers!
It works now. The solution was to initialize the TWI-port again. Because it seems like after adding the "TC - Timer Counter", the previous initialization was overridden. So, we had to set up the TWI-ports again in the conf_board.h.
We added this in the ASF/config/conf_board.h and now it works:
#define CONF_BOARD_TWI1 TWI1