So I don't fully understand what IEX does then. Let's say A puts 500 shares of AAPL onto IEX at $100/share, and B puts a buy order in for 500 shares at $100/share, but in between posting the BUY and the order executing (in that 350ms), they get more information, and decide they actually want to pull out, are they unable to?

Let's say B instead only buys 250 shares, what happens to the remaining 250 shares?

They are unable to do so. It is a queued system with a fixed transit latency through the queue of 350us. Any remaining un-executed of A is left on the IEX book.

IEX has this transit latency because they have order types that offer pegged execution, i.e. midpoints. A midpoint order is executed at the midpoint of the prevailing NBBO. The data required to build a view of the prevailing NBBO comes in from all other lit venues.

IEX has a 350us delay because they want to slow down the order entry side to give themselves enough time to make sure they are not pricing their pegged orders using stale market data. Simple as that.