Could it also maybe be related to interactions between 13 & 17 year cicadas?
https://cicadas.uconn.edu/#Hybrids says that hybrid 13/17 cicadas would either have a 13- or 17-year-cycle, but hints that the subsequent generation may be interesting.
The obvious outcome would be that the grand-children of a 13/17 year hybrid might re-hybridize back from 17 -> 13, or 13 -> 17.
If enough of the grandchildren stabilize on their new cycle, you'd end up with a 13 year brood 4 years later than the original 13 year brood, and a 17 year brood 4 years earlier than the original 17 year brood.