I assume that this person is sharing in a verbal way with other people. Yes, in this situation we have to be careful that we're not just seeking fame. Especially with Sympathetic Joy, as it is much more difficult for many Westerner's to share in this type of joy then it is for them to have Compassion/Lovingkindness for others. This is because the sharing of one's past generous actions could be perceived in a competitive way or as a way to put others down.
We have to be particularly careful about who we are talking to. Whether they understand what we're doing and can actually identify with what you are trying to do. We have to look into our own intention, are we boasting about ourselves in order to make others feel bad or are we trying to inspire others? If we are trying to inspire them, we have to be careful in what ways we inspire them. We need to be sensitive to the possibility that some people may be threatened by the goodness of others.
The most important person to share our past generous actions in order to inspire Sympathetic Joy is ourselves. If we can do this then we gain more happiness and it inspires others by our example. We need to ask ourselves the question, are we capable of having Sympathetic Joy with ourselves or are we actually sharing with others because we are seeking them to praise us? So, the most important person is ourselves first. Sometimes just by being here one can inspire others rather than having to talk about it.