You’ll need to initialize the Manager object like so, instead of using the sharedInstance:
CBLManagerOptions options = {NO, NSDataWritingFileProtectionCompleteUntilFirstUserAuthentication};
NSError* error;
CBLManager *mgr = [[CBLManager alloc] initWithDirectory: [CBLManager defaultDirectory]
options: &_options error: &error];
This changes the file protection mode of the database files such that they can still be opened by the app after the device is locked.