Can you post a pic of your sink? Having a hard time visualizing it. Sorry about your tile installer :-/
or you can use a nice flat 1x2 or 1x3 as a ledger support for the tile as well.I don't see why you can't have the tile start part way up the wall.
I would use a schluter trip piece along the bottom edge of the tile for appearances and it can provide some support to the tile while it sets.
Let's wait for one of the tile experts to chime in. I'm curious as to what they would say.