How can I attach the same footprint to subparts of the same IC in Altium?
You should not create separate parts in the library. Altium provides you with the ability to create sub-parts (multi-part components). This is popular for large ICs (i.e. FPGAs, or ICs with multiple independent functions), or ICs such as digital logic where you might have multiple identical gates in a single component. 

You can find a description of how to do this in the Altium documentation. Scroll down to where it says Creating a New Schematic Component with Multiple Parts.

Effectively, you start by creating a new component (just the first part). When that's done go to the Tools menu and select New Part. Alternatively you can use the shortcut T-W.



From there you can create your second sub-part, and repeat the "New Part" process as many times as you need.