This is the big difference of this new feature, that the operations to encrypt/decrypt happen on the client NOT on SQL Server. That means that if your SQL Server is compromised, the key pieces to reveal the data are NOT with the server. This means that even if your DBA wants to see the data, if they don’t have access to the CLIENT application then they won’t be able to see the values.
Always Encrypted strikes me as something that will be incredibly useful for 2-3% of the population, somewhat painful for 3-5% of the population, and completely ignored by the rest. I’m currently on the fence about whether, three years from now, I will consider “completely ignored by the rest” to be a shame.