The things your talking about are roots of a type.All of my CC's have them growing from between most segments,personally i cut them off if they get to unsightly but that's on my big plants.When propagating i take usually 3 segments,let them sit out in a cool,dry place about 4 days.This lets the segment that was cut or twisted (i twist) off the parent plant to callous over,preventing an opening for fungus to enter & they don't seem to rot as much. I only mist my cuttings,never pour water into them they will rot very easily if left in wet soil.I propagate mine in small solo cups & only mist every couple days at first.As they grow roots the soil will dry out sooner and the segments will thicken & stiffen back up,you may even see new growth a sure sign it's rooting well.They always grow the white roots from between the segments your talking about but i simply pay them no attention.I leave the cuttings in the small plastic cups until i think they have a good root system.I usually wait until the end of the summer to pot the cc starters unless they look stressed.
Sorry if i gave you more info than you needed but it wasn't really clear how far along you were with you cuttings!!! Hope i helped keep asking and someone who knows more than me will chime in.
GOOD LUCK !!!!
