How can the Advanced Composition Explorer (ACE) warn of incoming solar storms?
Solar flare X-rays travel at light speed, but the solar wind from CME's travels at merely 600 to 2000 kilometers per second. It's the wind that causes aurora and solar storms, depending on the orientation of its magnetic filed.
Here's a SOHO view of a CME. It's clear the gas is moving slower than light. You can tell if the earth is in the path of an ejection by how near to symmetrically the gas cloud expands around the sun.

So, to answer your question, the satellite measures magnetic field direction, and can give 15 minutes warning because the CME gas is moving much slower than light.