A lot of different names and correspondences can be applied to the "angels" for a lot of different reasons, but when I read Waite I don't get the feeling he necessarily saw them as angels but rather "influences." For example, in his description of The Lovers he says, "The sun shines in the zenith, and beneath is a great winged figure with arms extended, pouring down influences." He doesn't even refer to this one as an angel.
When describing Temperance he refers to it as an angel but then says, "I speak of him in the masculine sense, but the figure is neither male nor female" which gives me the impression that though he may refer to something in one way he may do so simply out of convenience. By "angel" he may not mean angel in the conventional sense. This is further demonstrated in his description of Judgement.
"What is that within us which does sound a trumpet and all that is lower in our nature rises in response--almost in a moment, almost in the twinkling of an eye? Let the card continue to depict, for those who can see no further, the Last judgment and the resurrection in the natural body; but let those who have inward eyes look and discover therewith." Here he refers to the angel as something "within us."
Outwardly they are viewed as angels by a lot people, but I think for Waite (and myself) they may have represented something more akin to mystic principles.