There's a reason for being picky about that. From a technical standpoint, "top" is just that, the top of the stroke, where the piston is at TDC. If you were to use the beginning of the compression stroke as the point at which to set the valves, for instance, rather than the mark indicating Top Dead Center, you'd have the crank about 80 degrees out of place, and you could get the wrong readings. Calling the start of the compression stroke the top can lead to confusion.
Plus, when you keep your references straight, it helps you understand what's happening within the machine as it works. The true top of the compression stroke can be felt through the starter too. If you bring the crank up against compression and apply a steady pressure to push slowly through the stroke, there is a point at which the resistance briefly disappears, the starter jumps downward a bit, and you feel what seems like a second compression stroke. The sudden drop in resistance was TDC. The "second compression stroke" is actually the piston, having pushed all the air past the rings, pulling a vacuum in the combustion chamber as it moves down the bore on the power stroke. The top of the compression stroke is where it ends, not where it starts.
When starting a manual decompression YZF, you are told to push the crank until you hit compression. This will occur in that engine at somewhere around 120 degrees BTDC, when the intake valves close. Then, you're told to pull the compression release and move the lever about an inch farther to stage the engine for starting. That moves the piston farther up the bore, but not past TDC, so that the remainder of the compression stroke is only about 70-80 degrees of crank travel, instead of 120, and you will be able to push it through that past the ignition point, and start it.
In an auto decompression engine, the AD mechanism holds an exhaust
valve off its seat until the engine is at the aforementioned 70-80 degrees before top, so it sets things up for you just by running up against compression.