Until somebody more knowledgeable than me answers this...

...you should probably post the following:

the wattage of your floro
the type/shape/physical size of your bulb(s), spiral or straight.
how much you paid for your timer - what make and model.

The packaging for my bulbs is long gone, but when I used them last year - I plugged a power strip into the wall outlet, then the timer into that power strip, then I plugged another power strip into the timer, and then plugged the bulbs chord into that second power strip. The bulbs and timer are still working fine.

My guess - and it's only a guess - is that timer circuitry has a microchip that might tend to wear out and die (not danerously) from the ballast action on your CFL.

If you already started 12/12 day/night cycle, then use two power strips and keep it going and keep an eye on things untill you hear from somebody more qualified.