An apparatus comprises a processing device configured to receive a request to restore one or more applications, the request specifying one of a set of remote copies of storage volumes that store data of the applications. The processing device is also configured to analyze the applications to identify (i) the storage volumes storing data for the applications and (ii) groups comprising the identified storage volumes. The processing device is also configured, responsive to determining that the identified groups are part of a group replication session, to select one of a set of different types of restore processes for performing the restore of the applications to the specified remote copy based at least in part on whether the identified groups comprise additional storage volumes other than the identified storage volumes and to perform the restore of the applications to the specified remote copy utilizing the selected restore process.