Each Festival race offers wristband points depending on how you place, (the higher you place, the more points you will be awarded with.) These points are used to progress through the different coloured wristbands and open new events. As this is the means of progressing the game, you will unlock each wristband naturally as you progress through the game.
You can always revisit any event you have previously completed if you did not come first, and try again to unlock the remaining points. Any festival event you have won will have a gold trophy next to the icon on the map, making it easier to identify what events you can win and earn additional points in. As the number of points you can earn is based on your overall position, set the AI difficulty to easy and turn on all assists.
To unlock the next wristband and its associated achievement, you need to drive to the race central bay in the Horizon loop after obtaining each new level.