Conversion Rate Optimization and Paid Media are very connected to each other and need to be part of the same agency / internal group, or worst case, a process needs to be put in place to connect the parties together. Conversion rate increases are not isolated to a landing page, the entire user journey will affect conversion.
Example: A user starts their product journey on a search engine. They typed in a keyword and were presented with 10 website options to click on. They chose an ad and clicked on it because that ad resonated with them. If they then end up on a landing page or site where someone else is testing ad copy that is not directly correlated to the ad they clicked on, you are going to lose that conversion. The landing page simply being relevant to the previous keyword or ad is not enough. The content needs to be a direct reflection of the previous action the visitor took.
There is another big benefit you will get with having Paid Media and CRO being part of the same team. The paid media person is testing ad copies and what gets the highest click through rate. If it is working on a search engine, and they are finding messaging/copy that has higher click through, then don’t you think the same content would also work on the website?
Make sure these two departments have a process to communicate and collaborate each other’s findings, and most importantly, don’t test ad or website content in isolation, which highly disrupts your user experience and inevitably hurts conversion rates.