What kind of headset jack is it?
"I think it has to do with the cell phones using true digital signals, and not analog, but how can a tone be sent to the cell phone and be heard as if you are physically pressing one of the cell phone buttons?"
The headset you are using, is it the kind that can be plugged into something else, general purpose so to speak? Or is it specially wired for your phone?
There is a transducer in that headet. That transducer is analog, probably electret. Now weather or not your cellphone accepts it directly at the input as analog, or if it is A/D-ed by the headset first, I don't know.
Regardless, even cellphones, at some point, have to convert sound from analog to digital. This is why DTMF can be triggered by a skilled "whistler" or "hummer" who can immitate the tones...via cellphone or analog set is immaterial.
If you have a spare headset, or if it is fairly cheapo, you should be able to take it apart, find the electret, remove it and wire your circuit in its place with the appropriate voltages, etc.