I’ve been noticing this a lot and let’s use a 13W Soft White (or what I call Blonde light) CFL
When it turns on it starts off like 2300K and eventually makes it to 2700K

Our CFLs warm up faster because we always have a fluctuating mains voltage (120-125-127-sometimes 130)
I don’t know if input voltage matters in order to make warm up faster

My Philips Tornado 23W/865 helical CFL, don't changes color at all when warming up, and so my Osram FH 21W/840 T5 on my ceiling, and my Osram Duluxstar Mini Twist 8W/827 CFL.

I seen that too, i think it is related to the discharge putting out less visible light compared to the UV output when cold, and possibly even different UV output between different bands (to which the Phosphor components react). Besides, there is quite some variation in the color (when fully warmed up) between CFLs of different types/manufacturers, that would be the same color according to their ratings

120..130V could make some difference in the brightness, probably only visible if the voltage changes while you are looking. It would not affect the color temp much