Legion followed after her to make sure everything went well. Despite how nonchalant they appear to be about the mission they gave her, they have a lot riding on being able to create a temple and how it is created.
A shrine is a personal dedication to a god. It is a symbol of the devotion of a single person or group to a god. Every local god gets one, be they evil or kind gods. But a temple signifies public recognition. Only righteous gods can have a temple.
A temple is oftentimes viewed as a public place of worship, but it is more significant than that. A temple implies that the believers of a god can come together to worship in public and don't have to hide. It means that the god is accepted as orthodox by the public. So a public temple is the divide between a religion and a cult.