You are bringing up an interesting aspect of Muggle / Magic interaction. There are aspects to a magical person’s awareness that lets them see things that Muggles do not (or cannot). The entrance to Platform 9-3/4 is one of them. The entrance to Diagon Alley is another. The phone booth entrance to the Ministry of Magic is yet another. One second a magical person is there. The next second they “are not”, and they go unnoticed by Muggles.
In my opinion, they are not actually gone. They have entered into what a Muggle would call a distorted part of their surroundings that are no longer linearly three dimensional. Platform 9-3/4 is there; it’s just not perceived in the normal sense by Muggles. There are other examples of where three dimensional space – taken as given by Muggles – are distorted to the advantage of magical people. The Knight Bus is an example (where it can get narrower to avoid a collision). The headquarters of the Order of the Pheonix is another. The Weasley tent at the Quidditch World Cup is yet another.
They “disappear” when the magical person enters the no-longer-linear space. To a Muggle, who sees only linear space, they “disappear”. To the magical person, who has the ability to enter into the non-linear realm, they either seem to enter a place that looks normal, or least tolerable (“Fellas, why the long faces? [on the Knight Bus]).
I am sure there are other examples.