I've said it before and I'll say it until I'm dead or I'm banned.
Timing is just one component of a swing.
Good timing and bad placement = bad result, both in the real game and in The Show. That's the way it should be. If irl Rizzo swung with good timing but too far under the ball, he'd pop it up or foul it back (or miss it completely), too.
This would happen in Zone as well. Bad PCI placement is bad PCI placement. It's just that in Zone, if you use it well, you can avoid terrible placements more often.
With Zone, you control timing AND placement. I assume that also works similar to real ball. Best lift is slightly under the ball. You impart an upward angle and back spin without wasting too much energy with a too high trajectory. "Influence" with zone is an odd concept because the "influence" should be your swing location + swing timing, both of which you have direct control over with Zone interface.
The best power is actually a pull-ish swing. JE/E swings. Good enough to still drive the ball and impart power in the swing, and it lets you really open up on the ball. This is especially true for a Pull hitter (look at their hit chart). Unless they took this out of the game, Pull hitters do better, especially for power, on JE/E than G timing.
Yes, the game is governing PCI location in Directional. That's a feature of the interface. Influencing in Directional is no guarantee. It's what you want the hitter to TRY to do. "Influencing" in Zone should be pretty much assured since you control the PCI. I would think it's just a matter of pitch selection or bat (timing) control (which you also need for Directional and influence since you always have bat (timing) control in your hands.)