I use a slightly different method. I hook up a remote starter button, and set the valves one at a time, starting at the front of the head and working back. For an exhaust, I crank the engine until the paired intake valve has opened and is almost closed again. This makes sure that the exhaust lifter is on the base circle. For an intake, I crank the engine until the exhaust valve starts to open, for the same reason. Don't get mixed up on which is exhaust and which is intake.
I make the adjustment, put a tick mark on the rocker with a felt pen, and move on to the next valve. When I'm done on that head, I wipe off the tick marks and do the other head. No firing order or which cylinders get adjusted in what position to remember, so less likely to make mistakes IMHO.
Hydraulic lifters can bleed down when the valve is held open for a short time, which is possibly why you're getting play after adjusting. Could also be that the lifter wasn't quite on the base circle during adjustment, which is why I use this method to make sure it is. Gets it done right the first time.