hey that's cool , I thought I was going to have to ake a video myself because I couldn't find anyone who does ends like I do ends but then TaDa a nice fellow was hiding away there on you tube :-)
If you look at the beginning and watch what he does with his straggly ends, tails. Then as he cahnges colour you see he holds the tails along the work so they get covered. That's how I've always done it and it's always been ok. How he fastens it off at the end is good too :-)
This next one isn't in a typical granny square it's in rows of double crochet (english treble) but she is sooooo good at doing weaving ends in and colour changing , very worth a watch.
Anyway I hope that helps a bit and will mean you don't have to sew the ends in, it also means you can carry colours up to use on another round rather than having to cut it off and start again.
Have fun :-)