Once you've activated rental marketing, all communication from leads goes directly to you as the listing agent, and account owner of the published property. We share these details with syndicated sites: contact name, contact email, and contact phone number. Beyond this, communication details are between agents and specific sites (Zillow, Trulia, etc).
If the lead sends a message through a partner site, that message will go directly to your email account associated with your Intellirent account.
See also: Can I hide my address when using rental marketing?