As I understand,
Caesarea has been the presumed
mint of the procuratorial coins by many numismatists since it was the seat of the
Roman governors.
Kushnir-Stein notes in
INJ 14 that most (all?)
Judaean bronzes from Jerusalem were struck on bevelled flans ("Some observations on Palestinian coins with a bevelled edge"). Since procuratorial prutot were also struck on bevelled flans, she is suggests they too were struck in Jerusalem.
Jerusalem
had a sporadically functional
mint from the time of
Hyrcanus I until at least Archelaus, so it would have made sense to simply continue minting coins such moulds were uncovered in
Caesarea (see Ariel's 2012 study "
Judean Perspectives of Ancient Mints and Minting Technology,"
INR 7). Consequently I find Jerusalem to be a more likely
mint than
Caesarea for procuratorial prutot.