The GTM itself does not determine how DNS requests arrive at one of its listeners - this is a matter for the NS records for your parent zone to point at the most appropriate listener(s)
There is one exception for this, which is where you have your listener configured on a floating IP address, which moves with the active-standby status of the LTM portion of the Big-IP. It would be highly unusual to have a floating IP address split between the east and west coast, so I assume you are not configured this way.
To put that another way, the initial lookup (to find the nameservers for the zone) is handled by the global DNS infrastructure, not by your GTM. The specific query for the A record for a service is then handled by the GTM listening on whichever NS records was selected.
If the client gets no response from that listener (for example, because it is shut down), then it would send the A query to the other NS entry. For that reason, you should ensure that all of your GTM listener addresses are included in your zone's NS entries.
Note that there's not really any concept of primary-secondary, or active-standby within GTM - all GTMs are always listening on their configured listeners.