I think the shot was close enough to wipe the tower out anyway, just like how Saw bought it on Jedha. Perhaps Tarkin didn't have an angle to directly hit the tower but take out the array?
This has been my theory... The DS comes outta hyper space, they likely aren't in the exact position to make the shot and the DS doesn't appear to zip along at sublight, so it takes them a certain amount of time to set up their shot. Time appears to be of the essence in some way too. Tarkin wants the leak sealed, orders the "quicker" (assuming) shot of just firing one reactor at the base as soon as they can. The angle comes in view, they take it, it isn't "direct" but it is the first shot they can take to destroy it, and it does... but it was too late anyway, and the plans were already up and on their way out basically. The Devastator (assuming) arrives, blockades what it can, but the final sequence takes place and they're off and running to ANH's timeline.
I like the notion that the DS's firing can go faster if you use less reactors to do it, but that in general the entire process is relatively slow. Even at Endor, they're not pew pew pew picking off capital ships, and I'm betting those aren't full power shots like at Alderaan, but rather single reactor shots on smaller-ish targets. One that can hit a slow moving target like a capital ship but can't pick off anything with great pinpoint accuracy either. I'd think that factors in. This isn't a scalpel after all.
Jedha they're directly above the city, just turn the dish down on it, badaboom... they had all day basically, but they also probably left quite a few people to escape who saw the writing on the wall I'd bet.