Yes, B will always go before C or D. He will also never go before A, assuming prompt jutsu on both sides.

The only time refinement matters is if B1 and B2 are both trying to use a jutsu at the same time. B1 will go before B2 because his refinement is better.

You can test this appropriately by unequipping all your gear and dueling someone with refinement. You can still go before some of their ninjas as long as your ninjas are further up the move order than theirs.

Also note that jutsu timing is a thing. If you wait to activate your jutsu until there's a lull in the battle, best time is just before the character's turn, then the jutsu will fire off instantly and not even give your opponent a chance to interrupt unless they're playing on Auto. Likewise, sometimes I switch my control to Auto to allow my interrupters to be on overwatch mode and scan for quick casts. Once people master timing then interrupts in general will fall out of favor and seldom get used. You can even ensure your slow casting non-prompt jutsu don't get interrupted by using them just before the character activates. Right before Sasuke takes his turn, I queue up his jutsu and then he uses it immediately because it's now his standard attack.

This also leads to the technique of jutsu HIDING. When your enemy uses screenwide jutsu or performs a combo, all other ninjas get hidden from view. This allows you to queue up powers without your opponent being able to SEE them. The result of which is once the combo or screen effect is over, your jutsu is ready and active and firing off next without your enemy having any time to target you for an interrupt. Doesn't work on laggers.
This post was last edited by Kyutaru at 2016-9-11 02:37

You actually CAN time an A jutsu, it's just a very narrow window and you have to know how laggy your enemy is. If your opponent queues up an interrupt before you even cast anything just hold off your cast until after his ability goes off. If you want to quick cast beforehand and he hasn't queued an interrupt then you have to wait until all the buffs are done.

Setting the game to Auto mode will effectively quick cast all the time as the AI doesn't choose a jutsu until the round officially starts. That's why it's basically impossible to interrupt someone on Auto unless you queued the interrupt anticipating the action. Because of this, I often set my game to Auto if I have Hinata and then if I see the enemy queue up an interrupt I disable Auto.

Best time to "time" jutsu is usually as the ninjas are going back to their positions after acting. Problem is due to server lag you might miss the window so you have to experiment and see when the exact moment is for you. I usually do it as soon as I see the last guy use his standard, just before he returns to his position. If you have zero lag whatsoever it's even possible to time it for the last possible second. Totally depends on latency at the time.

Neji usually hits first only because he's usually always in the front row position 1. So he goes before everyone if you have high enough initiative.

But put Guy in the back like position 4 and he'll never interrupt anyone unless they're using non-prompt Jutsu like Sasuke or Gaara.