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An intentional separation has a job
The Chimney Safety Institute of America's inspection guidance calls out the bond break around the tile where it passes through the crown. The point is to allow movement. A designed joint still needs a weather detail, so “leave every gap open” is no better a specification than “pack every gap with mortar.”
Ask for two separate observations
One observation is about the tile itself: intact, chipped or cracked. The other is about the adjacent crown and the condition of the joint. A loose piece of tile calls for a different assessment from a deteriorated joint next to sound tile. A photo looking straight down may not show both.
Compare the repair detail
Ask the contractor how the proposed joint will shed water while accommodating movement, and whether the larger crown slopes and overhangs the way intended. Put those answers beside the written scope. Leave materials, access and joint preparation to the person evaluating the actual chimney.