this app never reads any messages. the iMessage framework is very strict around privacy...so much so that you are unable to get user information of. This is why you will see Participate 1, 2, 3 instead of the person's name. There is no way to get this information of who the sender is! Kudos to apple for this.
The only message that is written to the chat is when you hit submit. There is no external service as all information is stored as metadata on the message itself. I did not want to have an external server (which has its own challenges, see in another message around collisions).
Your entire group can see the message but in order to interact with the poll they will need to download the app. They will be redirected to the app store if they do not have the app after clicking.