There could be something to this.
On the one hand, ordinary people don’t have a good grasp of how psychedelic drugs work. If you tell them you’ve given them what is to them essentially a mystery drug, one with a reputation of strange and complicated effects, they’re liable to become anxious about the onset of those effects.
Meanwhile, someone already feeling the effects of the actual drug may in fact simply be more at ease - either because they’ve already detected the expected effects and are acclimating to them, or because the effects themselves are placing the user into a less anxious state.