The problem is that transporters don't actually exist, so there isn't a "real" way in which they work. The show presented several different descriptions for how they worked, and the functionality had whatever feature the plot demanded.

So you get the ship's doctor who avoids it because she thinks it's basically as described in this cartoon, you get the copy of Riker from the time he Schrodinger escaped from that planet, you've got the autosaved DNA sequences that helped them reset after a virus was about to kill everyone, and you get teleported people perceiving their trip. All of that can coexist in just one of the mamy shows because it isn't consistent. Star Trek has some excellent detail, and explores some interesting hard scifi topics, but it's still just fiction.