AppDelegate.m

#import "TSTapstream.h"
#define MIXPANEL_TOKEN @"YOUR_MIXPANEL_TOKEN"

// ...

- (BOOL)application:(UIApplication *)application didFinishLaunchingWithOptions:(NSDictionary *)launchOptions
{
    
    [Mixpanel sharedInstanceWithToken:MIXPANEL_TOKEN];
    
    TSConfig *config = [TSConfig configWithDefaults];
    [TSTapstream createWithAccountName:@"YOUR_TAPSTREAM_ACCOUNT_NAME" developerSecret:@"YOUR_TAPSTREAM_SDK_SECRET" config:config];
    
    TSTapstream *tracker = [TSTapstream instance];
    
    // Call getConversionData to get the user's timeline history
    [tracker getConversionData:^(NSData *jsonInfo) {
        if(jsonInfo == nil)
        {
            // No conversion data available
        }
        else
        {
            NSError *error = nil;
            NSDictionary *json = [NSJSONSerialization JSONObjectWithData:jsonInfo options:kNilOptions error:&error];
            if(!json || error)
            {
                // No luck parsing the JSON
            }
            else
            {
                NSArray* hits = [json objectForKey:@"hits"];
                
                if(!hits || [hits count] == 0)
                {
                    // No hits in timeline
                }
                else
                {
                    // Hit exists in timeline
                    NSDictionary* hit = [hits objectAtIndex:0]; // Grab the oldest hit
                    if(!hit)
                    {
                        // Couldn't get any hits
                    }
                    else
                    {
                        // Get the slug of the Tapstream tracker that this user was attributed to.
                        // For a complete example of the returned JSON, including other
                        // data, please see:
                        // http://docs.tapstream.apiary.io/
                        
                        NSString* slug = [hit objectForKey:@"tracker"];
                        
                        // Set a Mixpanel super property called 'source' to the Tapstream tracker
                        // that this user was attributed to
                        
                        Mixpanel *mixpanel = [Mixpanel sharedInstance];
                        [mixpanel registerSuperPropertiesOnce:@{@"source": slug}];                        
                        
                    }
                }
            }
        }
    }];
    
    //...
    
    return YES;
}    

1. Where to put the code: The logic for this functionality should go in your AppDelegate.m, in the -application:didFinishLaunchingWithOptions: method.
2. How to call it without blocking: As shown in the example.
3. How to parse out the JSON: As shown in the example (iOS 6+ only).
4. What to do if nil comes back: This means that Tapstream doesn't know where the user came from; in general, the developer shouldn't do anything in this case (it's an organic user, or a user that hasn't converted yet).