  We describe the spreading property for finite transitive permutation groups
in terms of properties of their associated coherent configurations, in much the
same way that separating and synchronising groups can be described via
properties of their orbital graphs. We also show how the other properties in
the synchronisation hierarchy naturally fit inside this framework. This
combinatorial description allows for more efficient computational tools, and we
deduce that every spreading permutation group of degree at most $8191$ is a
$\mathbb{Q}$I-group. We also consider design-orthogonality more generally for
noncommutative homogeneous coherent configurations.
