EXIF stands for
Exchangeable Image File Format, and stores a lot of data from your digital camera. Orientation of the original picture can be one of the data items contained, values 1 -8
1:0 degrees – the correct orientation, no adjustment is required.
2:0 degrees, mirrored – image has been flipped back-to-front.
3:180 degrees – image is upside down.
4:180 degrees, mirrored – image is upside down and flipped back-to-front.
5:90 degrees – image is on its side.
6:90 degrees, mirrored – image is on its side and flipped back-to-front.
7:270 degrees – image is on its far side.
8:270 degrees, mirrored – image is on its far side and flipped back-to-front.
The problem is caused by the software that handles the orientation, especially web browsers. There does not appear to be a standard. It can also very sight to sight, I believe this site removes the EXIF data when it gets posted as user ORV suggested. This is most likely for privacy reasons
I suspect that when you crop your photo, change size and save it removes or updates the orientation data , just rotating and saving probably does not. You can also save as a .PNG file as it technically does not use EXIF data, although there is software that will preserve the data. There are EXIF editors where you can just change the value. Or find the orientation that is that matches up with your Cell Phone Camera, this is most likely the easiest.
-greg