What your describing sounds more like a "limited slip" type of differential if it requires the additive. These differentials usually use clutch packs, or cones that are forced out against the sides of the differential carrier. The additive is to actually help them slip a little, and allow for smooth operation. There are newer style limited slips that use worm gears that get forced out against the sides of the carrier housing when one wheel begins to slip, these do not require the additive. These types of differentials will never truely "lock"both wheels together 100% and will always allow for some one wheel to slip a little more than the other. This is why they are more desireable for street driving, because as you make a turn, your inside rear tire has to travel a shorter distance compared to the tire on the outside of the turn.
Now, a true locker, or locking differential, if its the automatic type, will physically lock both axles together, making your rear tires turn as "one". When you go around a turn, if you let your vehicle coast, the force of the inside tire traveling a shorter distance than the outside one will cause the locker to disengage, and allow those wheels to turn at seperate speeds, usually a "ratcheting"noise can be heard coming from these around turns, this is caused by the gear teeth inside it rubbing against each other. But, the moment you apply any throttle, these gear teeth will mesh with one another and lock both axles/wheels together, and this is what causes the "hopping" that is usually felt, or the front end to be "pushed"around. I imagine that in something with a wheel base as short as a garden tractor, this is much more nocticeable.
Now, there are also manual type locking differentials that obviously work just like the auto type, but it is engaged and disengaged by the driver, and I'm assuming this is what the op's tractor has. If not, and it is locked in all the time, this is really more like a "spool", more popular among the drag racing croud. This just locks both axle shafts together all the time, and if this is the case with the op's tractor, then Husqvarna is clearly marketing them wrongly. If thats not the case and it is manually controlled, then i don't see why Husqvarna should have to replace these transmissions underwarranty, they are just not being used properly by the owners. This is just the nature of a locking type differential, but if you are able to turn it off, then the differential should work like an "open" type and allow the rear wheels to turn at different speeds when turning. Sorry for the long winded rant, I am into offroading where lockers and limted slip's and how they work are kinda common knowledge among us, and I guess its just a pet peeve of mine when people get them confused. The names, or pet names that different manufactures use for their limited slip or locking differentials does not help any either, they just seem to confuse the general public. Hopefully this helps some people understand how the different types of differentials work.:smile: