USB hardware connection causing software reset
Typically the RESET# signal means that when it is asserted (LOW in this case, hence the sign #), a chip IC assumes all default values, all registers are set to whatever they are meant to be, clock is not running, nothing gets executed yet. The entire process inside the IC starts when the RESET# signal rises above specified voltage threshold, typical for the I/O buffers employed in the making of this IC. In most good designs this input has a Schmitt-trigger type hystersis, so only one good positive transition will be generated internally, giving the IC a clean start. 

If you need your IC running without regard if USB cable is connected or not, you should de-couple this signal from VBUS, and generate it internally, typically from some "POWER_GOOD" signal.

Having said this, it should become obvious that the RESET# should be "released" only after all power rails in the design have reached their nominal levels. In other words, the RESET# signal must be delayed relative to voltage applied to IC. If your entire design is "bus-powered" (power comes from USB cable), one simplest way to accomplish the delay is to put a capacitor across the 10k resistor, 0.1 - 1uF. This RC delay should be sufficient to start the IC cleanly. It also could be that the RESET# signal has internal delay, then it is OK to have it wired as per FTDI diagram. The details should be in corresponding datasheets.