If it is the new way, ask for the manufacturer specs and verify with them! Your picture isn't that helpful to me as I can't tell if any of that is rigid, or if it is all some sort of paint-on/topical application substance; nor what that substance is.

IRC 2012 mandates either continuous or step flashing. So if your jurisdiction has adopted IRC 2012, the continuous flashing conforms. Building Science Corp. in US Energy Department publications describes other acceptable approaches--including integrating a water shedding membrane behind the brick wall with the adjacent roof below.

Nevertheless, between continuous or stepped flashing, most experienced builders seem to favour the stepped approach.

The Code in my jurisdiction, OBC [Ontario Building Code] (see below) prescribes step flashings between masonry walls and shingle roofs.

This post was edited by worthy on Wed, Jun 12, 13 at 14:49

There are 3 issues: 1) how the flashing integrates with the shingles (whether short pieces of the flashing are "stepped" ie, inserted between the shingles or run in one piece under all of the shingles), 2) how the flashing integrates with the brick (whether short pieces are tucked into the brick joints and stepped down the brickwork or one continuous piece is mechanically fastened to the brick and sealant is added), and 3) whether the elements 1 & 2 are one continuous piece or two pieces (upper flashing overlapping the lower flashing).

The traditional and best method is to separate the upper and lower flashing so the upper overlaps the lower and to step them both. There should also be a flexible flashing installed against the bare roof sheathing and the bare brick (Grace Ice & Water Shield roof flashing or Perm-A-Barrier wall flashing set in Grace WB Primer)

If the better flashing detail was not in the contract documents and this kind of detailing is commonly done in your area then there's no reason to argue with this contractor and I recommend hiring another contractor to replace the work.