Firstly, the given tally procedure does not record nor report votes in terms of aggregate first-, or second-preferences, etc., and cannot be reverse-engineered to discover this. This is by design, and I would recommend against modifying the tally procedures to do so for the very reason underlying the question.
Aggregate first- or other-preference, etc. standings are irrelevant and misleading. All that matters is the relative standings of each candidate on a per-ballot basis.
Though we might mark each ballot in a first-preference, second-preference, and so-on manner, this is really just a shorthand way of indicating that the given voter prefers a given candidate more-than, the-same-as, or less-than other candidates.
A candidate X who is, say, second-preference and preferred more than candidate Y, on one ballot, affects the aggregate X vs Y result exactly the same as when X is first-preference and preferred more than Y on another ballot. The absolute “preference” numbers have no aggregate meaning – only their relative positions on each given ballot.
Accordingly, we capture and report only how many ballots have X preferred more than Y, Y preferred more-than X, or X preferred the same as Y. We do this for each pairwise combination of candidates.
So, with the given tally procedure, we never see that X “only” got so-many first-preference votes vs Y getting some other number of first-preference votes. And so this perceptual disconnect cannot arise. We see it here only because we’re making the sausage, and we see what’s going into it.
But even if the actual first-preference data were captured and reported, we would have the same situation in this respect as prevails where the Alternative Vote / Instant-Runoff Voting is used. And, again, I cite Australia1, where AV has been used for almost a century in national elections, and is in fact long and widely used in state and elections as well. In the case of AV, a lowest first-preference candidate can never win, but it’s still easily possible for a non-highest first-preference to do so; they seem to have been able to get past any perceptual disconnects about this.
Having said that, however, if the first-preference, and such, aggregates were indeed captured and reported, it would be important to explain these in proper context to avoid or counteract such misperceptions.