The modern Jewish calender was only established in the 12th century, supported by Maimonides. In the 1st century, the calender depended on observation of moons and ripening of crops as much as the sun. So variation was frequent, especially in communities further from Jerusalem.
Thing is, the idea of everyone sharing a calender or having fixed correspondances between calenders, is modern. Throughout Roman times there were multiple conflicting calenders in use, such as the Pompeiian Era in Syria, the Palmyrene Era, dating by Indiction tax divisions in Egypt, etc. Many were based on the Sun (as was the official Roman calender), but many were lunar or lunisolar, or even weird idiosynchronous ones (akin in nature to the 260 day Maya versions).
That a separated religious community might use their own calender seems reasonable, even probable. It is hard to show therefore any correspondance with the Temple or other Jewish calenders.
