If the designs have the same number of attributes and levels, and same number of concepts per task and #tasks, and the same DESIGN SEED, then indeed each design would be identical within a subject.
Remember, you set the design seed when you generate the experimental plan within our software. By default, it is set to a seed of 1. The simple solution is to generate the second CBC study with a different design seed (a different integer), and the third CBC study with yet another unique integer. That will create unique designs for each respondent, rather than having the designs be precisely the same due to the exact same setup (including seed) across the three conjoint modules.