When you record the Focus Time, the recording is saved in the Navigator>Animations tab.
Animations are saved internally rather than externally in Synchro, so there is no default folder path for Focus Time Recording. When you press record in the Play Ribbon you should see this window before the recording starts:
This window allows you to create a New Animation. If you have an animation already, you can record over it using this tool as well (as long as you have the animation selected in the Navigator). After you are finished recording you will see this window: