I think what makes a sacrifice throw in Toribash is slightly different than in real life, because in TB you can't literally fall to the ground and bring the other guy with you. I have always classified sacrifice throws as giving up your balance to execute the throw.

In regards to tani otoshi, and other throws in other directions, it really goes down to which way you break their balance. In my tani otoshi replays I broke uke's balance to their back, over their heels. In front sacrifice throws, you break their balance to the front, over their "toes".

I don't have a particular condition that must occur when I go for a sacrifice, what I look for to throw these is pretty basic:

For a front sacrifice, I look for times when uke is pushing into me, when makes it easier to drop under their weight and throw them over.

For a back sacrifice, the best time to throw is when uke has his back turned and his balance is weak.

For a turn-in sacrifice, I usually do it when uke has one foot on the floor and the other in the air, this makes it easier to rotate them around my body as they can't resist my pull with both of their feet.