Hi rainer,
I'm glad that you asked. The operative word here is "tonal." That is the clue to the approach I was taught. Most modern theory texts just simply state to write the elevated alteration going up (natural or sharps as the case requires), and lowered alteration going down (natural or flat depending on the key). I should specify here (if I didn't above) that I'm talking about writing chromatic scales. However, to make them reflective of tonality, there are two exceptions to the aforementioned practice: while ascending, write the lowered 7th rather than the raised 6th (to indicated the relationship to the subdominant), and when descending write the raised 4th degree rather than the lowered 5th to acknowledge the dominant key.

What do you think?

Am I correctly picking up your implication that these exceptions are not stated within the theory texts you mention (presumably because the texts' authors did not envisage taking tonality into account), but are modifications which those who taught you have "invented" and applied to the textbook rules in order to make them reflect tonality?I can see how that approach would help the reader identify the tonality of a chromatic scale if it wasn't already known, but I'd have to ask how often such situations arise. Also, one is more often likely to come across only a fragment of a chromatic scale than a complete one, and unless one is lucky enough for the fragment to happen to contain points at which modifications to the textbook alterations occur, one would be none the wiser. Does the approach have a purpose other than to inform/confirm what key one is in?

Two more flies in the ointment:

What if the tonality modulates during a chromatic scale? Would it confuse you to come across G# A Bb Bn C C# D Eb En F, or would it just tell you that somewhere after the Bb and before the Eb the key had changed from C major to F major?

The above rules are OK for major tonalities, but what about minor? How would you write an A minor chromatic scale? It seems irksome to have a note-letter appear in three different incarnations (sharp, natural, and flat), which it would have to if you raised the 4th(D) rather than lowered the 5th(E) on the way down: E D# Dn Db C B Bb A. And that's even before we think about what to do with/near the 7th. Do you want to distinguish natural/harmonic/melodic minor chromatics?

Rainer,
The method I learned is that found in A. Danhauser's Theorie de la Musique, (Editions Henry Lemoine - Paris c. 1929), Troisième Partie - La Tonalité, 13e Leçon: DE LA GAMME CHROMATIQUE.
In exemples given, it demonstrates the following: BOLD=chromatic alteration
Ascending Chromatic scale of C Major: C, C#, D, D#, E, F, F#, G, G#, A, Bb, B, C
Ascending Chromatic scale of C Minor: C, C#, D, Eb, E, F, F#, G, Ab, A, Bb, B, C
Descending Chromatic scale of C Major: C, B, Bb, A, Ab, G, F#, F, E, Eb, D, Db, C
Descending Chromatic scale of C Minor: C, B, Bb, A, Ab, G, F#, F, E, Eb, D, Db, C

A note in the text states that an A# in the C Major chromatic ascending scale would suggest the tonality of B major, a VERY remote key to C major, whereas the Bb suggest F major, a closely related key. Also, in the descending version, a Gb would suggest the key of Db major, a VERY remote key, whereas an F# suggest the key of G, a closely related key.

Note for example that in the ascending scales above E is diatonic in C major but chromatic in C minor.

Ascending Chromatic scale of D Major: D, D#, E, E#, F#, G, G#, A, A#, B, C, C#, D
Ascending Chromatic scale of D Minor: D, D#, E, F, F#, G, G#, A, Bb, B, C, C#, D

Additional text indicates that for instruments that are tempered in tuning (like the piano) the difference is strictly theoretical, the enharmonic notes being executed/sounded identically. But for instruments capable of the differences in pitch (the difference being a pythagorean comma) then the writers of such methods (for violin for example) are very particular to indicate the differences above (See for the chromatic major scale: L'Art du Violon by P. Baillot, pg. 68).

Isn't this stuff fascinating?! I love it! I thank God I had this lady to teach me when I was young. Was it old-fashioned? Yes, but then so is most of the music that I love and play!

Yes, this is indeed fascinating and you are lucky to have had an old-fashioned teacher.
I take it by "E is diatonic" you really mean the interval between E and the previous note is a diatonic (small) semitone. I'm not sure what significance you attach to how the E is approached.But would a violinist really play the "inbetween" notes at a higher pitch (C#, D#, G#) when ascending and at a lower pitch (Db, Eb, Ab) when descending, while playing all the other notes (C, D, E, F, F#, G, A, Bb, B) at the same pitch ascending as descending?