^thats actually not quite how it works. if you press your jump button after you do an aerial, or even at the same time, a DJC will not be performed. it also doesnt make the move come out faster, it just minimizes the time you spend in the air, giving you better pressure and mobility options, essentially like a suped up SHFFL.
In order to do a DJC, you have to do a double jump, then quickly do an attack afterwards, making sure that you are not holding the jump button which would result in a rising aerial instead. The timing of how quickly you perform the aerial depends on how high yoshi is from the ground, which attack you are doing, and if you plan to be exploiting his DJ armor. in general, the quicker you do an attack after the DJ, the quicker you will be able to cancel your vertical momentum, and quickly reach the ground (typically making it better for pressure).
whenever i execute a DJC, i usually hit up on the control stick (for tap jump) then use the c stick to do the attack, then roll the control stick downwards for a FF if needed. While using tap jump, you can hold diagonally left or right to shift your momentum in that direction very quickly. you can still get the same effects by quickly tapping x/y, hitting A, and holding a direction. Thats just a matter of preference. when doing DJC nairs, its best to just tap x/y then quickly tap A for max efficiency.
As far as application, yoshi will make the most use of DJC fairs and nairs for approaching and shield pressure. I recommend going into training mode, and doing DJCs over and over again to build up muscle memory. you will have little success if you try to just start doing it in a match, because you wont be able to control it very well. Its highly a matter of experimentation to see how the mechanics work, what kinds of momentum shifts you can get, turning yoshi around before doing so, and seeing how high in the air is optimal/how long you should hold the jump button before attacking at various heights. dont rely on informative posts to do all the work for you. we can teach you the basics, but you have to experiment with the mechanics yourself. What you put in is what you get out; its quite the technical maneuver, so if you are really looking to incorporate it into your game you will have to take matters into your own hands. once you build up the muscle memory for it, its really not difficult at all though.