We don't support anniversary based reviews out-of-the-box - the timelines for performance reviews are defined by each review cycle in the tool. While it's possible to create a separate cycle for each person being reviewed, it's not ideal.
We'd suggest a workaround of creating between 4 (one per quarter) and 12 (one per month) review cycles per year, and adding new hires from a given time period to that period's respective cycle. The fewer cycles you can use, the easier it will be to administrate.
You may need to be liberal with timeframes, and let people know when exactly you need results. For example you will need to tell an employee if you need his feedback before the end of his review cycle; this cannot be specified for individual employees via Small Improvements.