I have also seen two species of them in Rome, the rose-ringed and the monks (of which I have some poor quality photos) Climate wise, this is probably less surprising than northern Europe.

Exotic bird markets have long been a thing, so it may be that there have been many small introductions over the last millennia and perhaps further back, I found some references to Ancient Rome. Perhaps only more lately with warmer winters they have been able to establish proper breeding colonies. As an indicator species their movements might be quite telling.