Aha! This is my wheelhouse!
As far as I know, the Allies weren't too concerned with the creation of the Me-262. Why? Well despite the developement of the Me-262 starting around 1942 (where there were proper jet engines) by the time 1944 hit the Allies already were developing their respective jets. The US starting with the failed P-59 Airacomet (later producing the markedly more effective Lockheed P-80) and the UK producing the Gloster Meteor.
As for their reaction, I'm not entirely convinced that the Allies were surprised. Although from what I've read (and I still have the awful habit of forgetting goddamned every book name) the first sightings of the German Me-262 were via photo recon planes (namely the Mosquito) around late July, 1944.
As to whether or not the Allies knew, I am not well-read enough to answer it, although by 1939 there were already multiple attempts at the creation of jet engines. In Germany you had the BMW P3302 gas turbine prototypes, the Heinkel S series engines (which were rather weak). By 1940 the Junkers Jumo 004 and BMW 003 engines would begin development running into very very serious reliability problems due to fuel quality and material quality. Parallel to this however would be the British developments in 1940-1941 from the Power Jets V.1 (Whittle V.1) to the V.2 to eventually the Rolls-Royce Welland and Derwent derivatives.
And Parallel to that the shared developement in the US would produce the J31 and J33 General Electric jet engines that would drive the P-59 and the P-80, which were in all honesty just adapted Rolls-Royce Derwents.
So after this info dump what conclusion can I reach? It's estimated that by July 1944, the Allies already were aware that Germany had begun field the Me-262 via photo reconnaissance via the the British recon Mosquitoes (if someone could dig up the squadron that took those pictures I'd really appreciate it). As for the intelligence part, it probably was discovered although I'm not entirely sure the Allies found the Me-262 as a shock as much as there wasn't that much of a release of information pertaining to a potential new jet fighter given that Germany had quite the time actually commiting the planes to air.
Edit: Sources for easy access: