Since according to the timeline of when the Whitehouse was evactuated, this happened after the Pentagon crash, could be possible that he overheard them talking about the military planes coming to cover DC, or one of the later "hijacked" planes (iirc NEADS was up to about 9 by 10-11am), ie the orders being to protect DC rather than heading somewhere else.
There's a number of different options.
I'd tend to argue against the other mistaken hijacks as they appeared quite abruptly, very close to Washington DC. So they weren't tracking them.
The most likely explanation is UA93.
Tigerwall - the system used by the USSS to track aircraft, is capable of projecting the flight path of an aircraft based on its last known position, heading, speed, etc...
When UA93 went down, Tigerwall would continue to "track" UA93 until such time as someone removed UA93 from the system. The USSS would only do that once they had been told that UA93 had crashed.
NEADS, who, unlike the USSS, were in direct contact with the ATC Centres, were not told that UA93 had crashed until 1015, and even then they were only told because they specifically asked about it. (In other words no one contacted them to let them know).
The 1015-1020 time period is important. It's at about this time that people started finding out UA93 had crashed. It's also about this time that a shoot-down order was issued. It was also not long before this that the White House was officially evacuated (there were earlier isolated semi-evacuations earlier, but not a full-blown clearance of the site). Lastly, it was about this time period that UA93 would have reached Washington DC, had it continued at it's projected speed.
Thus, to my way of thinking, it's patently obvious that the conversation Mineta overheard was regarding UA93, and occured some time shortly after 1000.
The important thing to remember is the flight numbers. We're all very familiar with AA77, AA11, UA93 and UA175. We know where each flight was going, when it crashed, etc...
On the day, there was not necessarily a direct correlation. They would know a given flight was hijacked, and they would detect a potential hijack. Because we know everything, it's easy for us to identify which potential hijack was which flight. Not so for ATC and NORAD on the day. Each potential hijack alert had to be treated as a NEW hijack.
So when this conversation is occuring about the plane coming in, there's no reference to flight number. They don't know what flight it is. It's just an unknown radar contact.
Mineta allocated a flight number (AA77) to this conversation based on his understanding of what was going on. But he couldn't see Tigerwall. He didn't know what they were tracking.
So when the call came in that UA93 had crashed - probably some time well after 1015 - that probably WAS the first time Mineta had heard about a flight UA93 being hijacked. What he (and the USSS) may not have realised is that some of those early communications about unknown hijacked aircraft were ALSO UA93 so they HAD heard about UA93 already - indeed they had tracked it - they just didn't realise it.
-Gumboot