It appears that a very few Lumia 620’s have already come off of the line with the latest firmware on board. That’s perhaps to be expected, but it also looks like it’s this firmware that will bring advanced Storage management, including the ability to clear temporary cache files in “other” storage.
Currently, most Lumia 620’s are on the 1250 firmware. A few days ago, 1304 began to populate Navifirm and sure enough within the last day or so, 1307 has appeared for one device/region. It is that 1307 firmware that brings this new ability (we know only because we’re on 1304 ourselves). The OS though is the same Portico 10211 as found on current Windows Phones.