If you take the necessary steps, you can ensure that your music transfers over to a new device.
For iOS devices, make sure you have updated to the latest version of the Spinrilla app (3.5). This will sync your library to your Spinrilla account, and from there, you should have access to your library from any iOS device that you log into.
For Android devices, please use Google Backup to store any app data to your Google account. On the new phone, restore the backup from the service you backed it up to.