It's 100 percent visual timing, and having your eye and your finger on the flipper button in sync. You also have to make a quick assessment as to whether a drop catch is the best choice on a particular ball, determined not only by speed/angle but on table factors. If it's coming down at a high speed, depending on how fast a table is playing, you could just leave the flipper down and watch it bounce to the next one. You'll want this if the shot you want is off the other flipper, though if the speed and angle is right I will just backhand that shot instead of trying to catch, particularly if I didn't get the flipper in the air fast enough. The drop catch works like the opposite of a backhand, on which you are wanting the flipper to contact the ball full speed at the precise moment of the flipper's full extension. To drop catch, the flipper meets the ball in the same position but held up, to drop to the resting position with the ball, cradling it, breaking the fall. The egg toss/catch is a perfect way to look at it.
If it's coming off the tip end, you might just hold the flipper up and let it bounce to a trap, unless it's a very fast ball and the table plays fast or at a flatter grade, because this could send it into the outlane, or SDTM off a slingshot or another object nearby. Or, it could roll down the flipper, up the inlane and through the outlane. This is actually desirable on many older tables (EM and early SS) that have longer inlanes and would have a rollover score/bonus that can be triggered at least once, sometimes twice. On any pin like that, this can be more productive than drop catching. Double dip the rollover as you eye your next shot, then let it rip. Another risk with attempting to drop catch on any ball coming in at an angle toward the flipper tips/gap is if you misjudge and having the near side flipper held up might prevent a slap-save if it becomes necessary.
I love to drop catch just inside the midpoint of the flipper, let it roll for a split second and let it rip the other way for my wide angle shots, particularly off the right flipper in MB for the Creature or MM for the Catapult. It feels good as it happens in a fluid motion (especially if anyone's watching) but it's risky and it's one of the flaws in my style that keep my scores good but rarely great. I will drain balls prematurely and unnecessary through adrenaline-fueled recklessness. It's a really bad deal on some other pins like TZ, with its hungry right outlane and the left side posts that will feed poorly aimed shots to it or SDTM. Some tables reward behavior that others punish.