there's no button trick, and you don't have to be particularly fast to hit it either. but there are two nuances at play with that combo that people may not notice immediately, credit to wesballz for explaining one of them
the first is DI. if they di your shine too far horizontally they may fly out of reach of your dair, like kind of passing by it diagonally as they travel upward. hard di plus any amount of sdi on that shine and they are never getting hit by the dair period assuming a regular shine position
which brings me to the real nuance, shine position. tall characters (falco, marth, sheik, peach, falcon) are easier to hit with shine but realize that you can hit them with the shine at different locations. you can drop way inside them and shine the lower half of their body, like their legs, which will send them up farther relative to you, faster. if you shine their head then relative to you they will not be sent as far. youre going to be surprised at how much of a difference this makes. really surprised.
for shine double jump aerial, at high percent, go for the higher positioned shines if you want those moves to link up. at low percent, go for the lower positioned shines