This is a completely normal behavior. You set that option for the first time and on successive deployments the code-first migrations will take place on application start. EF (Entity framework) will start the Code-First migrations then.
Especially when you update your model manually.
You will not have to update your database manually. It will be done on application start. When your web-app is started, if you select the migration option.
Read more in detail here:
EF Code First Migrations Deployment to an Azure Cloud Service