The simple answer: Satellites do feel this force, but obviously don't get ripped apart. The tidal forces are simply too small (for the satellites' materials) to actually rip them apart.
The Why: Tidal forces happen because one side of an object feels such a larger huge difference in force than the other side. The magnitude of the force not only has to deal with the size of things pulling on each other, but the distance. Even massive things (like the sun or jupiter) have relatively little pull when very far away. If you get close, you feel the effects of them much more strongly and the effects increase more quickly!
Due to the fact that Io is a moon very close to other large bodies, this makes the difference of the force of gravity on one side is VERY different than that on the other. (Try plugging in correct values for Io, Jupiter, and the distance between them; then try calculating the force of jupiter on Io as seen from one side of Io to the other.)
Most man-made satellites around earth are much, much smaller than moons and they are surrounded by very distant or very small things. This makes the difference between the force of gravity on one side of the satellite is almost the same as the force of gravity on the other.
This being said, if a man-made satellite were to be in the same situation as Io, either being very large or being very close to other big things, it could get ripped to shreds.
In short: It's all about what forces are being applied. Distant objects apply small forces, close objects apply bigger forces. Tidal forces happen when gravity changes wildly between your head and your feet.