I used to work with a customer facing a similar requirement. Indeed it can always happen, that by different name resolution a client will be directed to the 'wrong' data center.
That´s why these folks implemented site specific cookies allowing to redirect to site specific hostnames.
As a result a LTM in DC1 noticed a client request with a cookie belonging to DC2. In this case it redirected to a hostname which was associated with a virtual server in DC2 only.
In my example above I forgot to discuss a fallback in case there is no match for the topology records.