I was looking for a way to automatically update the database after a deploy. The only way I found so far to do this, is to do this in code in your Startup class.
In the Configure method, use this code to upgrade your database other than Development:
if(!env.IsDevelopment())
{
db.Database.Migrate();
}
If you make sure to set the correct environment variable in the environment you’re deploying to, it will upgrade the database with your migrations.