No, the user does not need to pay for the update. Purchasing a promo code is just like buying an application.
Limited time prices on the App Store are just marketing words; they have no technical effect. No one has to pay when upgrading to a later version of the same application.
No, users will never have to pay to upgrade an existing application. Several companies decided that when they come out with a major update, they abandon the previous application and literally exit with a new application. This means that customers who paid for the previous application do not have an upgrade path and will have to buy a new application at the full price. Without noticing whether this is a good or fair decision by the developer, many existing users are ultimately unhappy with the cessation of updating the old application.
To summarize the key point: updates for applications are always, always free, regardless of which version you bought or how you paid for it (including the purchase of a promotional code).
In fact, this fact is unhappy. If developers can charge for updates, users will be able to choose whether to accept or not to receive updates. If they paid for the upgrade, data from the old version will continue to work in the new version. The main problem with the scenario described in No. 3, where the developer abandons the old application, and the “update” is really the whole new application presented in the repository, is that the data on the device is associated with a unique application identifier that was created with what makes it difficult or impossible to transfer to the new version (depending on how the developer deals with it).
The ability to offer free or limited free trials and charge for updates will help you plan plans that will usually be much better for consumers, while at the same time making them better for developers.