4 minutes is an eternity for any explanation based on atmospheric effects local to the Earth. It takes just 8 minutes for light to reach the Earth from the Sun.
On the other hand, .4 minutes is an extremely short period of time, relative to the total distance travelled by those gamma rays.
But there’s no need to draw any final conclusions right away. This result can and should be examined and debated from every angle, probably for years.
There may be a simple explanation : Here you have a narrow jet as a column moving outward at just under light speed. It slams into a cloud of neutral H/He gas. The front is convex, ie, the center punches through, pushing the gas radially outward and accelerating it to near light speed as well. Thus the outer rim of the cylinder is HOT and radiates in the gamma ray portion of the spectrum. At 4 minutes acceleration/delay time that’s about 75,000,000 km for the rim to hang back from the punch-through center of the jet. Thus the diameter of the jet can be inferred.
An alternate explanation is a concave/cup leading edge wherein the rim acts as a cutting knife, forcing the H/He gas into the center of the cup whereby it is accelerated to light speed. Thus it is a compressed mass that hangs back by .5 AU and heated enough to radiate in the gamma ray portion of the spectrum.
Either way there is your 4 minute delay being created in the shock wave of the leading edge of the blazer-jet. To wit, we don’t need to re-write relativity from this one observation, occam’s razor to the rescue...