HTM memory works by pattern completion. Many neural models work the same way and there is a considerable amount of theory to back up the utility of this computing model. Very few (none?) also handle temporal memory
Each map in the sheet of columns has (potentially) a vast number of overlapping learned temporal/spatial patterns. When the perception is registered the saved pattern that most closely resembles the sensed pattern is recalled. There is some parsing to distribute these memories & recall over the hierarchy
Why?
This acts as a filter AND directs attention to novelty. This goes directly to your attention point.
What is passed to the subcortical structures is a basket of features.
The initiation of action is a task delegated to these subcortical structures. The subcortex projects patterns to the frontal lobe to be unfolded by pattern completion in the varous maps until it reaches the central sulcus. This goes to your motor point.
By some relatively complex interactions, the expressive part of the cortex (frontal lobe) learns patterns that are further refined by the cerebellum to make the motor commands more flexible; this is still pattern completion.
Note that the recalled patterns are not tagged - there is no A=>B transformation in the HTM model.
The HTM pattern recall and parsing do extract central tendencies and present a crisp pattern to the subcortical structures. The fact that some pattern is NOT recognized is sufficient to distinguish novelty; the bursting behavior signals this to the thalamus, and through that, to other subcortical structures.