I've seen equipment manufacturers instructions that state you must twist conductors before using the supplied wire nuts. But from the instructions I've read on wire nut packages you don't have to, although when done they want 3 twists outside the nut.
I will answer by saying it depends on the manufacturer's instructions. As I have seen instructions that say "pretwisting not required" and "twisting of conductors required". I am going to try and locate the one package that requires twisting.
I have never seen the requirement of taping a wirenut.