Autoreset circuit for arduino - how I think it works
You are thinking about it all backwards.

The capacitor is discharged when you power up, as both sides are at +5V, so there is no potential difference.

When the serial port is opened by the PC the DTR line is pulled low by the FTDI chip causing a potential difference, and the capacitor to charge up.  This causes brief a low pulse on the RESET side of the capacitor resetting the Atmel chip.



(Image courtesy of Nick Gammon - RTS is DTR in your circuit [either can be used])

The value of the capacitor and resistor define how long the capacitor takes to charge up - the voltage has nothing to do with it.  However, the voltage applied to it does affect how long it takes to reach a different specific voltage - for example (made up figures here), apply 5V to it and it takes 1 second to reach 5V.  Apply 15V and it takes 1 second to reach 15V, so it would take only a fraction of that to reach 5V - but it would then continue past that 5V until it reaches 15V, which still takes a second.