XDJ-RX2 Beat Effects and Quantize

I'm a little confused about how this is supposed to work.

I know there are two different Quantize settings -- beat effects and deck (actually there are 3, since each deck has its own, but the two decks work the same as each other).

When I press the Beat ⬅ or Beat ➡ buttons, the Beat Effect timing goes to a round number of beats (e.g. 1/2, 3/4, 1, 2).  If I then turn the Time knob slightly, the XDJ-RX2 still shows this as the same number of beats, whereas if I turn it more the beat count becomes grey.  Does this mean that in one of the Quantize modes, the XDJ-RX2 will actually round the imprecise number of milliseconds to a round number of beats?  Which Quantize setting controls this?

Also, for some effects if you start out with Level / Depth all the way counterclockwise it doesn't really matter when you press the On/Off button to activate the effect.  But for others it does -- Trans will cut different parts of the sound, Flanger will start its cycle at a different point, and most dramatically, Roll will sample completely different sound depending when you press the button.  Does one of the Quantize settings control whether the XDJ-RX2 rounds the timing of my On/Off button press to the nearest beat (like the deck quantize does for pressing a hotcue, for example)?  If so, which one?

If I missed any other settings that could affect the timing of Beat Effects, those would be very helpful to know about as well.

Thanks!