So, here's some more details on triggering.
In manual (or preflash cancel) mode, all that matters is that the strobe sees one (or two) pulses. Try triggering at successively shorter pulses until the strobe doesn't trigger. Do that with the strobe on 1/16 power or less, so you don't overheat it. (Something that should be harder for YS-D3 than YS-D2; I've blown up several of those...) With the bright LED of my trigger board going through one of the nice thick Sea&Sea cables, Retra triggers with basically the shortest pulse I can send. YS-D2J (and D2, and D1) trigger with 4 us. YS-D3 won't even detect a pulse less than 35 us or so. If I shove the LED straight in the YS-D3 sync port, I can trigger it down to 5 us.
In TTL mode, the strobe actually has to measure the duration of the pulse. The photodiode circuit takes a little time to saturate and turn on its output, so the input-pulse-to-output-power curve has a bit of an offset to it. The strobe then takes that pulse length, and puts it through a lookup table to decide its output flash power. DS-TTL works by shifting the table up and down based on the power dial.
YS-D2 interprets a 23 us pulse as 1/256 power. Sometimes I can get it to fire at 1/512 - 1/1024 if I use a 20 us pulse, but it isn't reliable. 55 us = 1/32; 144 us = 1/8; 706 us = 1/2. Anything longer than 2400 us will dump the entire flash.
Note that these numbers are roughly logarithmic, because the strobe is designed to capture the output of a xenon tube. These tubes reach maximum brightness very quickly, and so flash power is just controlled by duration. Doubling the output requires double the duration.
Retra interprets 22 us as 1/32 power; 60 us as 1/8; 115 us as 1/2, and anything over 230 us as full power. That's why every time a new strobe model comes out, we have to profile the strobe to determine what pulse length will cause the strobe to fire at what power.
Now, on to the YS-D3.
In TTL mode, it can't reliably capture pulses through my sync cable shorter than 70 us. If I use shorter pulses, it *sometimes* will fire a dimmer flash. But most of the time, it doesn't fire anything.
It also needs a much longer pulse to reach higher flash power. Even a 940 us trigger pulse only causes it to fire at slightly more than 1/4 power. Which is a problem, because the strobe needs to capture the *entire* pulse length before it starts firing its own flash. If you want to use 1/250 shutter (which I do, on my a7RIII), the delay before the strobe fires means that the shutter starts closing before the end of the flash, and I end up with a black band on the top of my images. So longer than about 1000 us trigger pulses can only be used at 1/200 sec. Or 1/160 sec, if you need longer than 2000 us.
So, I turn the DS-TTL adjust knob up to +1.0. Now a 940 us trigger pulse will fire a 1/1 - 0.7EV power flash, 1050 us will fire 1/1 - 0.3EV (still usable at 1/250 sec), and 1200 us will fire the strobe at full power.
But by shifting the table up using DS-TTL +1.0EV, I lose some of the bottom end. 112 us = 1/8 power, 72 us = 1/16 power, and 50-60us = 1/32 power, but fails to trigger a lot more often than I'd like.
On top of that, sometimes the strobe doesn't trigger at all, even when I'm using 200 us pulses for both preflash and main flash.