It is a common requirement to align features in multiple layers. Topology rules help to identify features that are not correctly aligned. If the difference in alignment is less than the tolerance specified for the topology, features are automatically moved into alignment when the topology is validated. If the difference is larger than the tolerance, the misalignment is reported as an error to be adjusted by the user. It can be confusing as to when an error should or should not be reported.
Topology rules do not provide the ability to report errors when there are gaps between features of different layers. The rule "Must Not Have Gaps" applies only to features within a single layer. The closest rule to apply to this relationship between polygon layers is "Area Boundary Must Be Covered By Boundary Of." The rule is explained as follows:
"Requires that boundaries of polygon features in one feature class (or subtype) be covered by boundaries of polygon features in another feature class (or subtype). This is useful when polygon features in one feature class such as subdivisions, are composed of multiple polygons in another class, such as parcels, and the shared boundaries must be aligned." The rule produces errors where the boundary of one layer does not coincide with the boundary of the second layer, but does not assist in bringing those edges together.
For that task, use the Topology Editing tool, Align Edge. The features that are being aligned need not belong to the same layer; they must only participate in the topology together.