Summary: Tur vs. Tur, peshat vs. hanachon.
Post: According to the Tur's short commentary, shamayim at the start of Haazinu is a reference to the big cities and small towns.
"According to the peshat, the meaning of Haazinu HaShamayim is to those who dwell in the large cities which are fortified unto the heavens.; and vetishma ha'aretz is to those who dwell is villages and small towns."
Yet he does not offer this as peshat in his longer commentary:
"Some explain shamayim as referring to the angels who dwell in heaven, and the aretz as those who dwell on earth.
And some explain that this is on behalf of the rain which is from heaven, and on the earth that it should give its crops.
And what is correct is that it is the heavens and the earth literally, that the way of the pesukim is to take testimony from something which lasts and stands forever. And so too 'Hear, mountains, the dispute of Hashem' (Michah 6:2)."
It would seem that he changed his mind from one work to the other. I am not certain which one was composed earlier.