This is correct. Up front you want a selectable, LSD, or you want to verify how your automatic actually works.

The cheap kind of auto locker is some ratcheting teeth with springs. The basic mode of operation is that the teeth in the middle get pressed together when torque is applied to the assembly via the drive shaft. When you reduce the power going in the springs don't hold as tightly any more and the assembly ratchets around. The point at which this change occurs varies from locker to locker but the basic idea is the same. You see people say stuff like "let off the gas when going around corners". This is even more important for an auto front locker in slush, ice, etc as otherwise you can end up going straight.

 

With front and rear lockers engaged in snow/ice, there's a line. On one side, you go easy and make the corner. Then there's the line, which is fairly wide, where you give it gas and you keep going straight. The other side of the line is when you hammer the **** out of it and dorifto right through the corner.

 

I frequent the last line... just sayin

 

Most if not all of the popular ones work like this. The issue being you can lose control easier, because the tires will both break traction instead of just one. I have a lunch box in the rear of my xj, and it's pretty sketchy on ice and snow. My pickup's factory locker is of the type that locks after slip occurs, and is otherwise open. This type is much better for slippery roads.

I definitely would not put a non selectable locker in the front of a vehicle that is going to be driven on icy roads.