Osae means to push, stop, press, attach or seal.
In Wado, we do not oppose strength in principle. But, we do stop an attack before the opponent’s attack becomes powerful. Therefore, Osae Uke should be executed when the attack has no strength at the moment of contact, independent of style.
Torimi should intercept the attack before Ukemi has a chance to generate power. As Ukemi raises the knife his state is weak but unpredictable. It is very difficult to tell whether the attack will come straight down or in an angle. Hence, as Ukemi intends to cut down from above, it is time for Torimi to enter and execute osae uke, which is a state of power. At the same time, it does not matter whether Ukemi had planned jodan uchi or yokomen uchi.
The instant that you stop the opponent attack, it is wise to attack. He is not just going to stand there and odds are he will continue to attack. Ideally, execute Osae Uke together with an attack. These pictures are originally from my book "Wado No Michi" and at the time we chose to leave out atemi for the first picture. The reason is simple, now the attention is fully drawn to Osae Uke. Advice is to execute Atemi to the body and then step through to take the opponent down.
I was once told "you have to think: empi, power". I do understand the function of laser focussing your effort in order to give it your all... but in this case, I disagree. My students would never hear me emphasise the power of the arm and especially not techniques that rely on timing in the first place. Here's my advise on this particular one.