Of course the application allows DNS access. Not sure why you say it is IP only. Also, you can tap any station from the home screen to start a station manually.
Furthermore, the OS keeps track of the external vs internal IP and uses the correct one when appropriate. Which firmware are you on? You can find this on the About page.
Update: Also, external IPs are also numerical so even if it was IP only you could still remotely access the system. I noticed you deleted all mention in your original post about the IP issue since reading my reply however I will leave my reply here for historical purposes but for anyone else reading this the OP originally complained the app did not allow DNS based connections.
Update 2: Please note run-once program remembers the last run program allowing you to use the 20 min times as requested. Also, replying to the thread will make this visually easier than updating your original post each time.
Update 3: Please open a support ticket here to start a refund (also requested before the OP edited his post) if that is what you wish: https://support.opensprinkler.com. This is also the same site with the user manual and documentation on obtaining a Weather Underground API key. Please note we do not control Weather Underground and their site layout may change as they are acquired by weather.com. We will verify the documentation for obtaining a key is still valid.
Update 4: Please note you can also start a program using the hardware buttons on the device. For example, you can define a program to run all stations for 20 mins and disable the program (so it won’t automatically run) then manually run it using the buttons on the device when needed without using the computer or phone.