I think this all varies depending on the ship and the onshore concierge.
Our last trip on Celebrity, in a Penthouse Suite on Constellation, we received both a phone call and an email. All dining reservation requests (including Luminae at a specified time) were taken care of.
Our next trip in April is a b2b on Reflection. First leg in the Penthouse Suite, second in the Reflection Suite. No phone call, no email - I had to initiate by a call to the Retreat line. We requested dining reservations for each night at a specific time, and were told that they could not do that - and moved us to another time. I'm guessing our Butler will be able to change these for us, but bottom line is that our treatment was vastly different this time.