I own a recently built smart home. Last weekend I added LED under cabinet hard-wired lights using wires installed during the build. I changed out the regular switch with a Lutron dimming switch. The switch is on the same circuit as the overhead kitchen lights. Now my overhead kitchen LEDs will dim to almost nothing when I turn their switch off (not a Lutron switch) and have to turn the Lutron switch on and off to get them to completely turn off. Any ideas as to why and how to correct the issue?
There are lots on compatibility issues with dimmers and LEDs. LED lights are not as simple as the old incandescent lamps. They have little AC to DC power supplies (called "drivers") built into them because LEDs work on very low voltage DC power. Then there are literally dozens of different designs of "dimmers" and many of the electronic ones have what's called "leakage current" through them even when off. When used on circuits with resistive devices on them, like the old incandescent lamps, the leakage is so low that it is undetectable. But because the LED drivers are designed to be very efficient and the LEDs don't consume much power themselves, this leakage current is often enough to keep the drives and LEDs excited enough to "glow".
The solution is to only use dimmers that say they are SPECIFICALLY designed for use with LED lamps. These will usually have a detectable OFF detent in the slide / rotary knob that is used for dimming. The totally electronic type where there is no slide or knob are the type that usually don't work to totally turn off LEDs. So you either change out the dimmer or learn to live with it.
Traditional switches do not need neutral and did not have neutral wired to them. That changed in 2011 where neutral is now required at switches.
Dimmers are electronic devices that need power of their own. Normally powered devices get their power between hot and neutral. That doesn't work for retrofit dimmers, because neutral is not at the switch. So dimmers use a "hack". You can leak small currents through an incandescent without it lighting up. However LEDs are so efficient that this "intended leakage" actually lights up the light.
Your description of the device in comments makes pretty clear it's one of those (notably: blacks being interchangeable).
A separate issue: Some dimmers have a "hard off". They have smooth action through their dimming range, but in that range it's never quite off. You have to turn the knob harder - past a detent - to access a "hard off" which is a mechanical, absolute disconnect. This is a UX problem - people don't realize it's a detent, they just think it's end-of-travel. So they never turn the dimmer fully off.
A few dimmers have a similar "hard on", also past a detent. I had dimmers that made the incandescent bulb start to hiss or buzz after awhile when near full power; this was the answer on those.