Unless you fly perfectly over the station, you'll see that radial swing before you see full station passage
, but that swing means you are past the VOR.
For example, tidbits covered in the class included a view of the protected airspace for a procedure turn, a recommendation to use Pristine screen cleaner on EFIS, using station passage
on a LOC approach to know when to miss, many rules of thumb for airborne math like radius of a turn, and even "cheats" like landing in zero-zero (emergency only) on an ILS by keeping the LOC centered and on glideslope until mins, then using just 300 FPM until a gentle touch down.
It says elsewhere that flipping of the To/From indicator is station passage
. So long as he could logically support that he was in protected airspace and just too close to the VOR to have the needle recentered yet, we can't think of any reason why he couldn't descend.