How do Rosencrantz and Guildenstern react to Hamlet’s questions about why they are there? How does this give him a "heads up" to their purpose?

In act 2, Rosencrantz and Guildenstern arrive at Elsinore, tasked by King Claudius and Queen Gertrude to find out what is wrong with Hamlet. When they meet with Hamlet, they seem somewhat unprepared to respond to Hamlet's questions. They begin their conversation with small talk, but Hamlet almost immediately starts whirling puns and odd phrases at them. In line 260, Hamlet asks, "What have you, my good friends, deserved at the hands of Fortune that she sends you to prison hither?" The fact that Hamlet has called Denmark a prison confuses Rosencrantz and Guildenstern, who are having trouble keeping up with Hamlet's double-edged meanings.
After more talk of prisons, dreams and beggars, Hamlet circles back to his question in line 290, "But, in the beaten way of friendship, what make you at Elsinore?" Rosencrantz replies, "To visit you, my lord, no other occasion." His denial (that there is no other occasion) wasn't necessary. It would be expected for childhood friends of Hamlet's to visit him soon after his father's death. Rosencrantz has tipped Hamlet off that there is more to the visit.
He continues to badger them with questions and innuendos until Rosencrantz finally admits, "My lord, we were sent for." Now Hamlet can be sure that they are there to spy on him, and he will take advantage of that. Later in the play, Hamlet calls them "sponges" for doing as they are told and not thinking for themselves. He also says they cannot play him like an instrument, again showing he is always steps ahead of them. It is no surprise Hamlet is willing and able to reverse his own execution orders and have Rosencrantz and Guildenstern executed instead. Surely he did this in response to their betrayal, one that began with this initial meeting.