Your teacher's advice is consistent with the evidence.
The most natural source to use is Leopold Mozart. You will find that his recommendation is that all such short trills should begin with an appoggiatura.
From chapter ten which discusses trills:
Mit einem schnellen Vorschläge und Nachschläge spielt man alle kurze Triller.
That is, in this context, all short trills are played with appoggiatura and turn.
C. P. E. Bach is exhaustive and of great historic importance but should perhaps not take precedence over Mozart's father in this case. At any rate, he disparages beginning on the principal note.
Whether you play the flute or not, it is also very beneficial to read the essay by Quantz.
In your example, choosing the upper note start, you would play six notes or four, depending on the tempo. When the tempo chosen is most rapid, I am sure I have heard celebrated performers use only four. For example, I seem to remember Barenboim did this, simply adding an appoggiatura to the notated figure.
Added 8th May
There has been discussion in comments concerning the historical basis to beginning with the principal note. The question is: what evidence of the practice do we have from Mozart's lifetime applicable to trills like those in the OP?
A colleague has alerted me to the book Perspectives on Mozart Performance (1991) which contains an article by Badura-Skoda on Mozart's trills. This article discusses internal evidence in Mozart's works relating to the choice of trill execution: presence or absence of turn, presence or absence of appoggiatura, and so on.
I will not have an opportunity to consult this work at the library until next week. In the meantime, if any reader has it, please leave a comment.
A comment about Wiener Urtext edition raised the question of how we might decide for ourselves whether to start on the upper or principal note. Frederick Neumann in his Ornamentation and Improvisation in Mozart (1986) proposes this algorithm:
1) a trill starting with the upper note on the beat has
the effect of a short appoggiatura; 2) a trill starting with
a lengthened upper note has the effect of a long appoggiatura;
3) a trill starting with the upper note before the beat has the
effect of a grace note. We find guidance by leaving out the trill
and judging whether one of these ornaments would be a desirable
addition to the bare melody; if so, the corresponding trill type
is likely to be the proper or at least an acceptable choice.
Where none of these ornaments seems to fit, the main-note trill
is indicated. Where no clear-cut choice between one or more of the
alternatives emerges, more than one trill design will be fitting.
This algorithm still leaves room for difference of opinion in whether the substituted ornament is acceptable.