With single purchase of any product (theme and module), you are licensed to use the product on one store only. If they are running several stores on a single PrestaShop installation with prestashop's multi-store feature, you need to purchase a separate license for each store.

It's okay for you to use the product you bought on a development site. For people who are using our themes, here are two ways to do that.
1. Put the development site in maintenance so you can use all theme features with out registering it.
2. Register your theme on the development site so you can use all features,  when move the dev site to a live server, you can register your theme there again with the same license code, the dev site will be automatically de-registered. Another place to do de-registering is the "Downloads" page on ST-themes.