Each cellular provider has a different method to change the amount of time before going to Voicemail. They also control your Voicemail and the adjustments are usually made in seconds not the number of rings, before they turn the call over to the Voicemail.
Some people mistakenly believe that their phone is actually recording the voicemail on device and that is not the case. It is all done by your cellular provider.
We may be able to provide you the specific instructions or direct you to the correct site if we knew your cellular provider.