*supposedly you aren't supposed to twist the ends. I had an electrician friend that claimed that not twisting was the cause of bad connections. Paddedhat will be along to say why you should/should not do it. ;)
Well in this case your electrician buddy is not claiming anything, he is just stating the truth. A really well done splice will never have a wire "fall out" or fail for any reason, in residential applications, for the entire service life of the installation, which could literally be a century, or more. Pre-twisted conductors don't "fall out" and properly installed wire nuts, pre-twisted or not, don't allow a conductor to fall out.
Now the whole twisting thing is a bit of a controversy. The manufacturers will gladly prove and market the fact that their products do the job with "no pre-twisting necessary". Much like most of my previous bitching on the subject, IMHO, the reason for this is that pre-twisting is a skill, and like push wireable receptacles, this is another short cut designed to eliminate the need for a skill set, and assure that poorly trained Romex monkeys can quickly wire a home with little, to no, required talent.
A pre-twisted connection is something that can stand alone, without the need for a wire nut for any reason, other than to electrically insulate the connection. A properly twisted connection looks like a copper colored threaded bolt, and it is very tightly twisted, and symmetrical. The end is properly squared cut with a lineman's pliers, and the pliers is then used to grasp the very end of twist, and then spun, to round off the end profile, and put a bit of a "starter thread" on the bundle, to help the wire nut spring bite on, and start to thread. There are you tube videos on the subject, if you are curious.
That said, there is nothing wrong with skipping the pre-twist, for most residential work, especially if you are a DIYer. The reason is simple, because you are actually going to read the damn directions and do the work properly, which is way more that the average Romex monkey does. There are a few secrets to non-twisted connections. First, it's critical to keep the stripped ends of all the wires even and tightly grouped, before you start the wire nut. Now the nut needs to be installed with a bit of effort, Grasp all the wires in one paw, and hold tight, twist the nut on like you mean it. Push it hard into the wire group and twist it tight! Keep twisting until nut is making the insulated portion of the wires start to twist together, now continue until they are twisted at least a full revolution and a half, or more. One final trick. A combination of solid and stranded wires can drive you half crazy. First, pre- twist the stranded wire. Nothing elaborate, just spin it with your fingers so it's got a nice twist to the individual strands. Now lead the stranded wire by a bit. Hold the solid wires so the tips are even, and let the stranded one stick past by 1/8" or 3/16". Don't get too upset if every so often an attempt to properly install a wire nut turn into cursing, and throwing things. Sometimes they seem a bit possessed, and determined to not go on properly, just to spite you. The best way to deal with this is the throw the wire nut away, you already stretched the spring, and it isn't going to heal itself. Clean up the grouping, make sure the ends are even, and if a stranded conductor is involved, be darn sure that there are no stray little strands plaguing you. Start again with a fresh nut. Good luck.