How to use software flow control properly so as not to overrun the devices input buffer

I am trying to write to a serial port that is communicating with a device that uses software flow control. The device only has an input buffer of 512B, but I often need to transfer large strings to it over serial (~200KB). I've set my serial object's FlowControl property to software, but writing a lot of data overflows the devices input buffer. After transferring all the data, I examine my serial object's input buffer to find many XON and XOFF characters intermingled with other text data sent from the device.

I thought that MATLAB or the OS would handle the flow control at a lower level, but it seems to be ignoring these XOFF characters and continuing to send data. How can I enable software flow control properly?