There is no way to "tune" these remotes. Secondly, and correct me if I'm wrong, but if you try to train the Apple TV with a button that sends only one command per button press, it just sits there with the progress bar incomplete.
Anyway: Not important, eric, I just solved the problem.
Iâm pretty sure of that myself. But, that doesnât change the fact that the Android ecosystem is pretty lame. Iâve owned Android devices in the past, the OS feels almost childish when compared to Apple. Not a fanboy or anything, some Android hardware is pretty good, but itâs overshadowed by the inferior OS running the devices.
I would have to see a video of this behavior to know exactly what youâre seeing, but that doesnât sound like how it operates for me.
Which behaviour do you mean? The Apple TV IR remote learning or what it does in response to learned codes?
I just programmed a GE/Jasco programmable remote to the same codeset as the MX-500 (I used a Pioneer DVD codeset, as that had all the buttons I needed). Same behaviour. Now it could be because I trained the ATV with the MX-500, and the MX-500's expression of that codeset is b0rk3d. I'll try re-training the ATV from the GE/Jasco remote tomorrow and see what happens.
AIUI, when IR remotes send a stream of commands, they send one non-repeating block, then repeating blocks. That way receivers can tell the difference between multiple button presses and a button held down.
If I have that right: Somebody, somewhere, is doing something wrong.
Can you train your MX-500 with the Apple TV remote using the Learn Method?
The Apple remote is Bluetooth. The MX-500 is IR. So, no.
Just get yourself an Apple TV 2 or 3 IR remote. They can be found for less than $15.
I had one from an old Apple TV that I had... they work just fine. Although, now that I'm used to the touch remote... I actually prefer it over the older apple tv and newer fire tv remotes. I find the fire tv buttons to be a bit stiffer than what prefer.
The reason for the MX-500 universal remotes is the one remote can control everything we want: TV, Apple TV, Blu-ray/DVD player, DVR+, receiver, digital input switcher, and X-10 controller. No remote clutter.
Plus my wife and I each have one at our seating positions, thus no "pass the remote" nonsense.
They work fine with everything but the Apple TV. Even then: They work acceptably with that, except with the Channels app.
Besides: It's not just the IR remotes. We really don't like much of anything about the way Channels works on Apple TV, as compared to the way it works on Fire TV and Android TV. To the point that, if I had another HDMI input, I'd probably hook the Fire TV back up just for Channels.
You can also turn off the skip button if it's bothering you.
Okay (shrug).
Ah, I'm sorry, you're right. I had forgotten that I had old Apple TV IR remotes to train with that I have used in the past.
So I tried training the Apple TV from a GE/Jasco "universal" remote I had. Programmed the GE/Jasco remote to each of the two "Apple TV" codesets they have, and the Apple TV complained that the up and down navigation buttons were the same codes 
Then I found one of the Panasonic DVD codesets on the GE/Jasco remote was nearly identical to the codeset I'd been using for the Apple TV, except they induced a pause in repeated codes, after the first transmitted code, when you pressed and held a button. So, for the nav buttons, I taught the MX-500's from the GE/Jasco remote.
Last step: Turned off that annoying on-screen "Skip" button.
Now everything appears to be working acceptably.
That was all much more involved than it should have been.