The answer depends on the person displaying restlessness.
According to DSM-5, written by the American Psychiatric Association (2013) emphasis mine
A mental disorder is a syndrome characterized by clinically significant disturbance in an individual's cognition, emotion regulation, or behavior that reflects a dysfunction in the psychological, biological, or developmental processes underlying mental functioning. Mental disorders are usually associated with significant distress in social, occupational, or other important activities. An expectable or culturally approved response to a common stressor or loss, such as the death of a loved one, is not a mental disorder. Socially deviant behavior (e.g., political, religious, or sexual) and conflicts that are primarily between the individual and society are not mental disorders unless the deviance or conflict results from a dysfunction in the individual, as described above.
In other words, the problem has to induce distress and/or problems functioning in personal, social, work or family activities over a prolonged period of time.
So in order to answer your question
Is the restlessness mentioned a psychological phenomenon to address?
the question that needs to be asked is does it meet the criteria set in DSM-5?
If it does, then it needs addressing in therapy. If it doesn't, then there is nothing to address.
An aside to the whole situation you have brought here, I wonder if these "indicators of restlessness" are actually something else.
I wonder if they are actually there in body language terms, indicators of interest.
The symptoms they exhibit are pressing own body parts, adjusting hair, folding hands
I know I thumb my chin or bottom lip when engrossed in, or (during a re-reading of a passage I just read) thinking through, what I am reading. This is not restlessness. This is intense interest.
References
American Psychiatric Association. (2013). Diagnostic and statistical manual of mental disorders (5th ed.).
https://doi.org/10.1176/appi.books.9780890425596