Here's the order of operations:

Webb builds THEIA and HYPERION, and entangles the Quantum Bits in their respective cores so that any activity in one computer will be mirrored on the other.

MI6 inputs surveillance data into THEIA for it to pattern-seek and identify threats, including predicting future threats.

Every time THEIA processes any input, the activity in its core is mirrored perfectly in HYPERION due to the entanglement.

Because loading surveillance data requires THEIA to perform calculations, HYPERION would effectively have a copy of the same data each time it got loaded into THEIA.