In s TX (z9a) I bring in garage when my lows are in the 40s. To be on super safe side I'd bring in at 50s

I'm also in SoCal (western edge of the IE) I just yesterday picked up some more cuttings from a neighbor that put them out for free (yay!) and this time of year what I usually do is fill a pot with proper planting mix, thoroughly saturate it with water and then let it drain for a couple days, plant the cutting, put the pot in our unheated laundryroom and forget about it until Spring when it sends new leaves out. The occasional humidity from doing laundry keeps it from drying out and shriveling.

I would consider some sort of heat mat to help with the rooting process but other than that I don't think 60s should be a problem.

Thanks for the tip on the heat mat, just ordered one on Amazon (surprisingly affordable). Although now I wish I had started all of my cuttings in bags rather than some in pots (so that I can get more on the heat mat).