The GPS almanac is a table of the exact orbital information of every satellite. Every receiver needs a copy of the almanac to understand where the satellites are supposed to be, so that it can determine where it is in relation to those satellites.

When their clocks all shift one minute simultaneously, the almanac isn’t updated. Every satellite is 60 seconds away from where the almanac says it should be.

If the satellites were geostationary, receivers would still work, they’d just be off by 0.25 degrees of longitude as the entire constellation would be shifted the same amount. But the GPS constellation consists of satellites in a variety of inclined orbits. Nothing is where the almanac thinks it is, and nothing is where it is supposed to be in relation to anything else.

Parent comment is correct: GPS will immediately fail, and remain down until an updated almanac is published and distributed.