It depends on the manufacturers instructions/requirements for the seat. We have a Diono Radian and it has a tether strap but it is optional to use it (rear or forward facing) - although it probably gives you a better install if you do.
I'm not sure what 'tether compatible' means - you'd probably have to look a bit more into the instruction manual for the particular seats to see if it is optional or not.
Just a note, using LATCH does not change whether or not you have to use a tether, LATCH replaces the seatbelt function rather than the tether strap. Our other carseat, an Evenflo Symphony 65 is installed with LATCH but is still required to be tethered when forward facing.
We really like the Radian, it is a bit expensive, but can be used as a booster also so we wont need to replace it. Rear-facing it takes up a bit of room so you'd need to make sure it fit in the car first (we use it rear facing with our 2 year old and you can get an angle adjuster to make it a bit more upright and hence to take up less space). It is a long seat which is good for us as I have tall boys (with a 6 foot 6 DH).
We also like the Evenflo - seems a bit more comfy when they are younger as more padding around them. Both my boys have been in it as babies. My oldest would have outgrown rear-facing in it (height, not weight) by now and we wanted to keep him backwards a bit longer so hence why we got the radian. The Evenflo also can be used as a booster so again will last a while. It is quite high off the seat so an older child might find it harder to climb into than the radian.