I put cuttings in a cup of water three days ago, the largest cutting is already showing initials. Two smaller ones are also showing some but not as many as the big cutting. I'm new to water rooting, but this seems exceptionally fast.

I put a large branch in a five gallon bucket of water two weeks ago no roots but its a double branch and is making new leaves. Your doing grate in 3 days. Do you keep it inside. Mine is in a greenhouse with both doirs open so it dont get hot. I am in Louisiana

It's inside in a windowsill for now, but it's plenty warm for it to be outside. We were 87 degrees today. I plan to put it outside as soon as it gets some real roots.

Are you sure those are root initials? Looks to me like swollen lenticels. 

The picture is too blurry to tell but the white spots are far more likely to be lenticels than roots.  Lenticels improve oxegen uptake in a low O2 environment.

I'm new to rooting in water, and to rooting where the roots can be seen...so it's very possible they aren't roots yet.

I had some successes in rooting in water, but lost about half to rot........ So if its a fast rooter, water is OK to start them.  A variety like Panache which is not as fast would not do well in water.

I checked the "roots" again today, many just fell off. I assume that means they are just lenticles. There are some on the very bottom of the cutting that look different though, not grainy like the others.