I finally set up my DAW Remote at Logic (somehow my serial number for Cubase AI was lost, so I couldn't get it downloaded, so I use LPX), and while DAW Remote lets me click Record/Stop/Play with no issue, Track Control seems to not work. For example, if I click F1 to Add Instrument Track, it's not doing so.
Is it a Cubase-only thing or is it that I did not set it up right?
Yes, the items silk-screened on the front refer to Cubase. The F1 and other function buttons defer to Mackie Control - please see how Logic Pro X allows you to assign the Function and SubFunction buttons. They become F1-F12 for Mackie Control protocol. Most likely you'll be able to assign these as you require.
In the MOXF Data List booklet, page 117, you'll find the list of functions concerning Logic Pro and the front panel.