Could be a lot of things, but let's go through it.
When the toilet would not stop running, did the water overflow into the overflow riser? It may be that you did need to replace that flapper and now you are dealing with a second issue.
My knee-jerk reaction is that if the Korky is kind of sticking when it's turning off, then perhaps the float isn't reinstalled correctly and is binding a bit as it shuts off. I would just do the process again. Turn off the water at the toilet. Flush. Pull off the refill tube (which, presumably, is daylighted above the lip of the overflow riser; otherwise that could cause the toilet to continue to run). Pull off the blue cap on the 528. Pinch the float arms like tweezers. Remove the float. Twist off the cap. Pull out the interior tube. Pull the strainer out of the bottom of the tube. Rinse everything. You can even wipe a bit and make sure everything is all clean. Then, reassemble: white strainer back in tube. Tube back in valve. Cap back on. Reinstall float. Make sure that you hook it in so it moves freely. Test that it's freely-moving. Blue cap back on. Refill tube reattached. Turn water back on and see what happens. You might make sure that the water valve at the wall is all the way open, as well.
Have you seen the video from Korky on how to service the valve? It's helpful to watch someone else do it: