My experience has been that there are definite "seeding" points for Barbarian landings and it looks like the one you describe is one of them. The timing of the appearance should be random but of course that does not rule out consecutive appearances although the most I have experienced is about 3 or 4. Civers have naturally taken advantage of the likely seeding points for
1. stationing their Diplo to bribe (bargain priced) Barb units desired at the time (eg a Trireme for a landlocked OCC city) and
2. planning their trap for the lucrative Barb Leader capture bonus
although the consecutive landings can be challenging to say the least.
BTW Oldman your absence is much missed in OCC - hope you will have time for another scenario