The Stoic way includes empathetic reactions, i.e. groaning/moaning outwardly, in moments of shock. Both because it is a natural reaction even the perfect sage cannot help against and because he should help others to overcome their feelings.
A.A. Long has something to say on this in his book Epictetus: A Stoic and Socratic Guide to Life (OUP: 2002).
First, let me give you his translation (p. 230):
Do not hesitate to sympathize verbally with a [distraught] person, and even, if the
occasion arises, share in the person's groans. But take care not to groan also within
He explains the text afterwards (pp.253-54):
Epictetus would not be a Stoic if he thought that the proper way to help a distraught
person is to 'feel' that person's pain. The task of a Stoic comforter is not to become
upset oneself but to try to assuage the afflicted person. But, as we see in the
passage printed at the head of this chapter, Epictetus does recommend 'showing'
sympathy in words and even 'sharing in another's groans', provided that one does not
'groan within oneself' (Ench. 16).
What are we to make of this controlled empathy? There are two sides to Epictetus'
recommendation. First, an outward acknowledgement of the distraught person's
distress, putting oneself in the other's position; and, secondly, an inward refusal 'to
be carried away by the impression' that the other's situation is objectively 'bad'.
Inwardly, comforters should say to themselves: 'It is not what has happened that is
crushing this person but the person's judgement about what has happened.'
Epictetus admits that no one, including the ideal sage, can fail to react emotionally to
quite unexpected shocks, such as a thunderclap or sudden news of some
catastrophe (fragment 9). Such things can happen too rapidly for any reflection or
judgement to intervene. But he does not take such uncontrollable reactions to count
against the difficult Stoic doctrine that dread and other debilitating passions fall within
the scope of our volition. Even a wise man will blench under a sudden shock, but
blenching is not an instance of dread, as the Stoics define that passion: 'judging that
something terrible is looming.' Having experienced a terrifying shock, the wise man
'does not assent to such impressions or add that judgement to them, but rejects them and finds nothing to dread in them'.
Stoic comforters, then, will allow for shocks, but they will take prolonged distress and other passions to be self-inflicted, deriving not from events directly but from people's
misjudgements about the harm or benefit they are experiencing or expect to
experience. (bolded mine)
In short: While a good stoic should always be able to offer help and empathy to people who are in distraught, they should never be carried away by the experience of either the emotional distress of others or their own. Stoics know that the pain is not objective, but only arises because of the personal judgement of the situation, so judging the situation as not necessarily and persistingly affecting oneself - even if it does in a moment of shock - is the Stoic way. This includes helping others to do so. It prevents the persistent manifestation of negative emotions and enables us to be happy.