MK3 Suspension...
 

It is possible the spring was not seated absolutely perfect on your car or maybe the springs on your buddy's car has been on there longer so they have "worn in" so to speak.

As for TEMS, not all Supras came with it, my Supra doesn't have TEMS either.

Not all supras came with tems.
If it's not in your dash and console you don't have it.

If your front end looks awesomely low. Then ya they may have reversed them but ya, it may not have seated propperly. So take it somewhere and get it looked at. Don't drive it all janked up. You're bound to make something worse.

Stick with what you have because it's probably already set to sprt mode which is where mine stays unless I'm over the road driving and then I play with it and it does make for a smoother ride.

But once you start adding sway bars..., eh. You can get by without it.
You're rigid.

If you want a softer setup you can manually adjust the valves, I believe the details should have come on an insert with the shocks. Otherwise it should be available on their website. Nothing wrong with manually adjusting if the car is a daily driver... Plenty of owners pull the TEMS system... so you can buy most of the components and add them. It's a fair amount of work though, and you may want to find out why people don't like it first.

To check the springs just count the coils... Compare to your friends. IIRC the rears have a couple coils less.

It sounds more to me like his rear coils may be sagging or have been cut. The Eibach Pro-Kit is a raked setup... the rear sits an inch to an inch and a half higher. It is possible to exaggerate if the coil is twisted so it's not fully seated in the perch... get under and look and the perch and where the coil ends and you'll see where the coil should be resting.