Conversion occurs when a user completes a transaction. Since transactions take place in the online store this is also where conversion is tracked.
In order to attribute transactions and revenue to a certain source, different reports can be used depending on the tracking solution you are using and how attribution is set up.
Because Publitas hosts the online publications for you, by default, the website will register traffic coming from the catalogs as referral traffic. To allocate sales to catalog-traffic you should be able to find the catalog-domain (view.publitas.com and/or your custom domain) in the list of referrals.
TIP: If you're using Google Analytics to track your website, be sure to also check out Appending UTM tracking parameters to all links (Beta).
If you have cross domain tracking enabled, navigation between the website and publications is not tracked as referral traffic. In this case, you can create a segment that includes users that have opened a catalog and maybe even interacted with it.
For example:
Include > Page > contains > /page
AND
Include > Event Category > Exactly matches > internal links