I guess the license could be interpreted either way:
Each product is licensed for use by a single entity on web sites owned and/or controlled/managed by that entity.
In the case of sites being managed (your customer) by a designer (you), the intent is: Each product is licensed for use by a single entity on web sites managed by that entity.
As soon as you drop management of a site, then it needs a license. I think this is a typical operational model – a developer builds/manages a site for a customer (the owner). As long as the management is active, the developer’s license (usually multiple site license) will cover it.