I come from the line of thinking that, when boundaries are crossed, the time to address the issue is immediately. In the case of this person asking where I'm going to be sitting, I would probably say, without getting emotional, rude, or confrontational, the following statement:
I have that covered. You can find me in the flex space area if you have anything you need to report to me. Now, let's get back to business on X...
Since you're not responsible to this person, you need not provide any explanation; instead, just matter-of-factly move on. People like this say things like that to try and get a rise out of you, so if you keep your cool and keep your power by not getting defensive, then it takes away their power and may hopefully make them stop. It also just makes them look bad if there are undertones of hostility on his part but not on yours.
Afterwards, it may be a good idea to talk with this person in private, ideally after the meeting. Remember, the sooner issues like this are confronted, the better. After the meeting, take this person aside and calmly explain that you don't appreciate the "Jane sightings" and that you'd appreciate the person stop. It may be possible he doesn't know he's doing harm, and even if he does know, calling him out on it privately may get him to change his behavior.
As others have said, if the behavior doesn't stop, then you'd need to escalate it to your manager or HR, but I also believe that, as a manager, you need to demonstrate that you are capable of handling personnel issues and personality conflicts on your own.
Dr. Henry Cloud, clinical psychologist and leadership coach, in a Forbes article titled "How to Manage Boundaries in the Workplace" answers the following question:
What happens when a co-worker oversteps your boundaries and does something that upsets you? How should you respond to them?
This is a great example of when a team has a vacuum of leadership boundaries. The best thing to do would be to use the “symptom” as an opportunity to talk about some values and behaviors that the entire team could covenant together to implement in situations like this one, and then they would know what to do. For example, the value might be “Honest Conflict Resolution” with some agreed upon behaviors that would bring that to fruition, such as “when we have an issue to resolve with someone, we go to them directly and seek resolution. We receive and listen when someone brings an issue to us. We always seek an answer that is good for both.” That kind of value before hand, with these specific behaviors, would lead someone to know what to do, not only in that situation but others as well.
In summary, what Dr. Cloud is saying is that you need to set the expectations on how you will be treated, as well as how other employees are treated when there is a conflict. You have an opportunity to set that standard. Lead by example, and don't allow people to treat each other this way.
Finally, on that same note, you can also start by addressing these issues between subordinates on your team. If two of your subordinates call each other out publicly or if employee A announces an employee B sighting or does something similar to embarrass that person, this would be a great opportunity to call out this behavior, but without you being the target of the bullying or the conflict.
