The hitter's counts when these long balls were hit
The pitches from Yu Darvish on these home runs: fastballs at 94-96 mph
Three of the four hitters were ahead in the count, one was in an even count.
A large part of why major league hitters are as good as they are is because they are smart and prepared. They pounce on opportunities. Each hitter knew the count/situation. Each hitter was in a dead red fastball "don't miss the heater up and out over the plate" mentality. It doesn't matter if the fastballs coming were 85 mph, 95 mph, or 105 mph - they would have not been tardy on the fastball in the location they were looking for.
These pros know the pitcher is in a position to where he doesn't want to fall further behind to a 3-0, 2-0, 2-1, or 3-1 count and is likely to throw a fastball to try and even the count or get ahead in the count. And more often than not when a pitcher needs to get himself back in the count it's not going to be a fastball on the inner half. So as a hitter it's wise to look for something up that's middle, middle out.
If you've ever watched batting practice at a pro baseball game there is a plan and approach for each of the three or four rounds of swings each group gets. The first round will consist of some bunts, hit and run swings, and get 'em over situations. The next rounds will have more focus on line drives - balls that are driven deep with authority. These are the type of swings you'd want to take if you were 100% sure a fastball down the middle was coming.
Teach your kid to be extra prepared when ahead in the count. Practice this during BP or even when you're hitting off the tee or doing soft toss with him/her. Before you throw some BP pitches or set certain balls on the tee, prompt your kid they are to react and take a swing in a favorable count situation - 1-0, 2-0, 2-1, 3-1, 3-2, as examples. In those counts it's time to be prepared, take your best swing, and not be tardy. If your kid/kids you coach take good aggressive swings and miss the ball or foul it straight back, that's okay because they were in the right state of mind. If the ball is fouled off to their opposite field side (first base for a righty, third base for a lefty) then you'll want to make a correction because this signals being late on the pitch.