The Conjuring 3 dramatizes the real-life possession cases of David Glatzel and Arne Johnson, but in doing so manipulates their timeline. It's not exactly surprising that The Conjuring 3, subtitled The Devil Made Me Do It, isn't entirely based in fact, despite having its roots in reality. The Conjuring movies haven't been shy about stretching the definition of being inspired by a true story, and that's understandable, especially considering how successful the franchise formula has proven to be. Reality doesn't always come complete with enough excitement or surprises to fill up a movie script.
In the case of The Conjuring movies, there's another consideration in play too, and that's the real-life reputation of now-deceased occult investigators Ed and Lorraine Warren. The Warrens' work has always had a loyal following, but at the same time, many people who've encountered them over the years say that they were essentially con artists. In that sense, it's perhaps best to treat the onscreen Ed and Lorraine more as characters and less as people.
Real-life Warren controversies aside, it's undisputed fact that an exorcism was performed on young David Glatzel, and that Arne Johnson went on to murder his landlord. The Conjuring 3 just sees fit to alter exactly how long it took for those two things to occur in reality.
The Conjuring: The Devil Made Me Do It states that the Warrens participated in the exorcism of David Glatzel on July 18, 1981. However, there are several things off about that compared to the real timeline of events. For one, the Warrens claimed that David was possessed by no less than 43 demons, and the boy ended up undergoing multiple exorcisms, not just one. The exorcisms also took place in 1980, including the final one where witnesses allege a demon left David and entered Arne Johnson. However, a considerable number of months went by before Arne murdered his landlord, which happened on February 16, 1981. That's of course still months before The Conjuring 3 is set. Arne was ultimately convicted on November 24, 1981.
While no concrete reasons have been offered for these timeline swaps, there are a few likely explanations. When it comes to moving back the timeline to the summer, that may have been to avoid duplicating the winter setting of The Conjuring 2, as well as avoid the hassle of having to fake winter, since the film was shot in the far-from-snowy state of Georgia. As for the decision to compress the overall time between David's exorcism and Arne's murder, that was likely done for narrative expediency more than anything, as having only a few days pass doesn't allow much respite from the terror for the characters. This is especially true for Ed Warren, as his heart attack and recovery are a big part of The Conjuring 3's plot, which would've changed considerably had he already been recovering for months before he and Lorraine set out to find and stop The Occultist.