Hello,So long as the tpk resource is in your project, maybe you could try to display the resource this way? I was having similar problems and this solved the issue for me. Also make sure that your tpk file is included in your copy bundle resources.
NSString *mobilePath = [[NSBundle mainBundle] pathForResource:@"YourTPKName" ofType:@"tpk"];
AGSLocalTiledLayer *tiledLayer = [AGSLocalTiledLayer localTiledLayerWithPath:mobilePath];
[mapView insertMapLayer:tiledLayer withName:@"Choose a name here for access later" atIndex:0];