It prevented it by having a hardware module on the CPU's memory controller that AES encrypts the contents you are sending to DRAM, and decrypts it before reading it back to the CPUs memory structures. All with hardware keys completely invisible to software (and one that is basically impossible to manipulate physically).
And you need to be able to do it multiple times for the bits of memory that you want to snoop on, to be the bits that survive the transfer.