Not always....you would have to take the available AIC and then calculate the let thru. Your breaker mfg can assist or may have info already done
See 110.9, and 110.10, and in your case it could be a series rated system so review 110.22 B, and then 110.24
As already stated, if the 22 kA breaker is required because there's 22kA available at that panel, then the distribution breakers need to be 22kA-rated, or listed with the main breaker in the series rating tables published by the manufacturer. If there are other 10kA breakers in the panel, then maybe they're series-rated with the main.
The other code reference is 240.86.(B) for tested combinations.