I know I answered this on Twitter, but for the benefit of anybody else having the issue:
A lot of photos (including those taken with iPhones) have rotation EXIF data embedded in them which some applications respect and some ignore.
By default, ImageKit won't do anything special with EXIF data. However, if you use the Transpose processor, it will read the EXIF metadata and apply the rotation it specifies.
More explanation is available here.