Why On DMR and other digital repeater systems, a talkgroup is a logical channel identified by a numeric ID that is carried in the digital data stream. Your radio's codeplug entry for that channel has to contain the correct talkgroup ID (and time slot and color code on DMR) so the network knows which conversation you want to hear and transmit into. Once the ID is programmed, you simply key up; there is no human gatekeeper on the repeater deciding on a per-talkgroup basis.
Watch out Registering is a real step for getting your DMR ID in the first place, but that comes from the radio ID issuing body, not the local Frequency Coordinator or the repeater control operator, and it is separate from selecting a talkgroup. DTMF tones are analog touch-tone signaling used for autopatch and control functions, not for digital talkgroup selection.
Digital = data. Talkgroups are selected by a number in your codeplug, not by a tone or a phone call.