Don't provoke, don't pursue...
I think you took the mature & proper response for the most part.
As a licensed security officer in a # of locations & types of details(estate security, office bldgs, hotels, medical centers, govt offices, etc) I can tell you many people get mad or lose control of their emotions then when confronted by LE or bouncers/security are so spun out they deny even saying or doing anything.
I'd advise any license holder or gun owner to AVOID unstable people. Leave or ignore them unless they block your path or you can't leave the area.
Remember too that safety = distance.
Smart phones or a DV type compact recording device can help you document a unstable subject's threats or acts. They are worth the $ to save legal fees, false arrests, bogus EEO complaints, etc.
Do not follow or chase subjects either. In my local area, there have been 3 incidents where "concerned citizens" got involved, 2 of these citizens were seriously hurt by the violent felons.