You can use the Apple Lightning to USB Camera Adapter and a USB cable to connect your iPad directly to your JD-Xi. If you do this, you will see "JD-Xi" as an option in the MIDI Ins and Outs in Patch Base. To work, you must also make sure that the JD-Xi is using the "Generic" USB driver. To do this, on your JD-Xi (taken from the JD-Xi manual):
Use the Cursor [<] [>] buttons to select “SYSTEM,” and press the [Enter] button. The setting screen appears.
Select “USB Drv” and use the Value [-] [+] buttons to change the setting to GENERIC.
Press the [Exit] button several times to return to the top screen. The edited parameter is saved when you exit the system setting screen.
Turn the power of the JD-Xi off, then on again. After changing the “USB Drv” setting and saving it, you must turn the power off, then on again in order to get the system to operate correctly.
Patch Base manages the data in the JD-Xi in a slightly different (but hopefully more flexible) way than the menus on the JD-Xi itself do.
A Program on the JD-Xi is essentially like a "Performance" on an older synth: the Program stores your Effects settings, as well as pointers to which Digital, Analog, and Drum parts will be loaded from the JD-Xi's memory. So, when you save a Performance, you're only storing these settings. You're not storing copies of the actual Digital, Analog, and Drum parts as well.
In the Parts editor at the bottom of the Program editor, when you select a Part, you're just telling the JD-Xi to load the sound that is stored in that memory location. The names you see in the dropdowns for selecting parts in Patch Base are based off of the latest data you loaded in the Bank editors of Patch Base. So if you haven't fetched the banks from the JD-Xi, those names won't be correct in the dropdowns.
Patch Base 3 uses a different structure to manage sounds on the JD-Xi, letting you save Digital, Analog, and Rhythm parts individually. But if you used Patch Base 2 and had saved Programs in the app, those will now be listed in the "Legacy" section of the app.
When you load one of these Legacy programs, a bug in the JD-Xi switches the Program to use the Vocoder, which will cause issues for Programs that don't use the vocoder. But to fix this, simply go to the Program editor in Patch Base after you've loaded your Legacy program, and change the "Vocal FX" switch to "Off". This should restore your Program to normal functionality.