Of course Stravinsky was aware of his polytonal writing, while most of it was diatonic. Mind that all composers - and especially those of the 20th century had a development of composing, considering harmonic, rhythmic and tonality aspects: Important stylistic devices of his music up to the 2nd War were polytonality and a distinctive rhythm, sometimes including quotes from popular music. Stravinsky also composed serial works in the 1950s. There are many different influences in his music, which he merged into a distinctive style.
Andrew J. Browne writes in his JSTOR article:
"The general conception in England of Stravinsky's work is peculiar
and misinformed. It seems to be readily assumed that after writing
L'Oiseau de Feu ' and ' Petrouthka ' Stravinsky plunged into chaotic
dissonance and brutal rhythm, and has latterly come to the surface to
parody Handel and Massenet. Stravinsky has said that ninety per cent.
of the hostile criticism levied against him hails from England. He is
mistaken. We do not pay him the compliment of criticism : we treat him
like a naughty child who likes to shock his elders (and bettors). He
is not to be taken seriously; he is part and parcel of the Russian
ballet, a company of freaks and practical jokers, anything but
artists. Stravinsky, in company with Epstein, enjoys the distinction
of being ' news ' for the British Press. Above all, Stravinsky is an
experimenter. The English abhor experiment in art; they prefer
imitation of tradition. Even the few who treat Stravinsky as a serious
artist see in his music predominantly the force of rhythm and
percussion. For them ' Le Sacre ' is the starting-point. Now, ' Le
Sacre ' is the one isolated work in Stravinsky's development. It is
concerned with dynamics, masses of tone-colour, blocks of sound; a
huge orchestra is employed, and the writing for it is vertical. All
Stravinsky's other works are written for small and selected
combinations of instruments, and the writing is horizontal.
Stravinsky's real contribution to modern music lies in his polyphony.
His melodic invention is of greater import than his rhythmic ingenuity
and his harmonic diversity; indeed, his rhythms are conditioned by his
polyphonic part-writing, and his harmony, always diatonic, has
steadily veered towards classical moderation."
Aspects of Stravinsky's Work
Andrew J. Browne
For further reading:
PhD - A Theory of Harmony and Voice Leading in the Music of Stravinsky [1981 Straus]
Conversations with Igor Stravinsky (Craft, Robert)