There are a couple things to note about using Infusionsoft Affiliate Tracking:
Leads will get assigned to the proper referral partner when the Lead opts in, but when using the API, the referral partner will not be able to see that the number of optins they have increase. This is a limitation of the API as addressed by the Infusionsoft development team at http://community.infusionsoft.com/showthread.php/5271-Referral-Tracking-Showing-No-Opt-in-for-API-Optins?p=18016&viewfull=1#post18016
The referral partners will get credit for purchases though. If this is a major issue for your referral partners the workaround would be to use the Custom HTML e-mail form embed you can get from your Campaign Builder form editor instead of the API e-mail integration for that page. You can learn more about how to embed Custom HTML forms at HTML Form Integration.
The other important thing to be aware of is setting up your links properly to work with the API in your Referral Partner Links area. Infusionsoft offers a guide on how to set them up at http://help.infusionsoft.com/userguides/referral-partners/set-up-a-referral-partner-program/track-referral-activity-via-the-api
Please also see this Q&A Webinar about setting up affiliate tracking with Infusionsoft in ClickFunnels