For a non-Apple using fan, they may not get the joke as The Apple CEO’s Apple logo icon was only visible on iPhones, Mac Computers and Apple devices. On a Windows device, it is blank square; on an Android device it would render as either a blank gray rectangle or an X-ed out.
Tim Square is definitely not the connotation the Apple CEO was going for as Apple personnel typically refers to its own devices and software over all others. However, Apple had no comment on the query about the logo mishap, if it was indeed a mishap.
Meanwhile, in the White House, it seems that they are engaging in some damage control. The official transcript of the meeting, there is a hyphen between the words “Tim” and “Apple” as if there was a pause between them and that the president was meaning to thank both the Apple executive and the company itself.