Libraries like Accel stepper usually use raw STEP and DIR signals. If you want to use that kind of interface with the Tic controllers, you could configure the input mode to “STEP/DIR”. More information about this can be found in the “Setting up STEP/DIR control” section of the Tic user’s guide. Note that the STEP and DIR inputs are connected to the Tic’s on-board stepper motor driver IC; using them to control the driver bypasses the Tic’s speed-limiting and acceleration-limiting features, and the Tic will have no knowledge of the current position or speed of the stepper motor.
If you want to use the Tic’s speed and acceleration-limiting features or have it keep track of the position of the stepper, you could instead use the TTL serial or I2C interface to send a “Set target position” command to your controllers.