No, users will not have to pay to make the searches on the app store. Instead according to the report, Apple is said to be considering allowing companies/developers to pay them to have their apps shown at the top of search results. This would be similar to what Google is currently offering for webmasters to have their websites listed at the top in the form of ads during searches.
In a way this is good as it could allow developers to have their apps listed in more search results. For example an app related to football might not have football in its title, but by paying Apple to return its app in search results related to football could be allow developers to pull in more users. The downside is that we can only imagine that search results could end up being rather spammy with unwanted apps, or it could end up misleading users.
However we suppose the app store does need to undergo changes and improvements as time goes on, so we wouldn’t be surprised if such a feature was introduced. Assuming that this is what Apple has planned, there is a chance we could learn more about it come WWDC which is scheduled for the middle of the year.