In the film it is shown that Alan Turing used the cracked information to decide which German attacks should be prevented, while letting others occur without intervention. I am wondering if this is an accurate depiction of true events, and whether Turing really 'played God' while deciding how to act based on the information, or is this an exaggeration of his true control?
Also, did Turing get any recognition during his lifetime for his contribution to the war, or did the secrecy of the work prevent his efforts being recognised?
In a word, "no". That scene (like much of the film) is a dramatic construct, Turing had little if any involvement with the distribution of Ultra material such as Enigma decrypts. David A. Hatch reviews The Imitation Game in the NSA's Cryptologic Quarterly 2015-01 Vol. 34, and as he says of that scene:
"The ULTRA decrypts were distributed by the military to a select group of cleared readers, mostly senior commanders and their intelligence officers. The commanders were required to come up with a cover plan to disguise the source of their information before they could act on it. In real life, for example, Allied commanders, who were remarkably well informed about their enemy, would order unnecessary reconnaissance or patrolling to fool the Germans about their intelligence. Despite a number of myths, no one’s life was sacrificed to protect the ULTRA secret."
Another of the myths Hatch mentions is that Churchill 'allowed' Coventry to be bombed to bombed to protect Ultra, which I cover in a previous post along with a bit more on naval Enigma (Was there a specific incident where Engima information was withheld on purpose?)
In terms of recognition, his wartime work remained secret until 20 years after his death, his obituaries only referenced his mathematical and pioneering computing work. It was only with The Ultra Secret and Bodyguard of Lies in 1974 that the breaking of Enigma and Turing's role started to come to public notice.