Well if it picked up more than you wanted with a landscape rake, then it will most likley do the same thing with the rock bucket you showed.
I am sorry I didn't elaborate more but There is no quick way to do this unless you pay someone with a powered rock picker to come clean out the rocks and breakdown the chunks of sod. It is not particularly labor intensive using a tractor, but it is time consumeing.
Since you rototilled a grassy area there is probably a considerable ammount of sod and other plant roots that are binding the soil together. What you described sounds like these root wads(and the attached dirt) won't pass thru the rake and fill it quickly to the point where the whole thing acts like a rear blade. Think of the rake as a screen on a shower drain, if it is clogged with hair, then the water(soil) backs up.
The key here is to keep at it with the rake, particularly in this warm dry weather. Set the rake at an angle and let the material spill out one side or the other into rows, then go back and hit the rows again and roll/tumble them again and again. By disturbing those clumps of root and soil and rolling them around, the soil in the roots drys out and the movement causes it to fall away leaving a light clump of root to be more easilly collected with the rake. The rolling action of the rake tines causes the lighter organic material to come to the top once the soil is broken out of it.
You could also try a drag harrow to help breakdown the clumps of root/soil. You could also use the rototiller some more, just not going so deep as to pull up more undesturbed soil. This is basically what the powered rock picker I mentioned does, it shakes and breakes the material so it will pass thru a filter screen returning the soil and leaving the rocks and other large debris behind in the picker.
As the sod root bundles get broken up, the soil falls thru them leaving the root wad on top. You then set the rake for a light pass removeing as much of this root material as possible without loading the rake up with dirt. Here is where the gauge wheels come in handy as they allow you to more precisely control the depth of the tines as the tractor moves up and down over the as yet unleveled arena(doing this will start to level the area). As these root clumps are removed and the soil is broken down into individual grains like sand, you will be able to go deeper and deeper with the tines to filter out the rocks without clogging the rake with soil.
Untill you get the rootwads broken down and out of the soil, anything with tines that you drag thru the soil will collect these clumps of roots and they in turn will act like hair on the shower drain. This can even happen on much wider tine spaceing. I built a 60" fork bucket last year for working on getting material onto and reforming older brush piles. It has eleven 2" boxtube tines with 3.75" spaceing between the tines(seen on my avitar pic). I can easilly fill it with dirt that has enough organic material in it to cross the gaps in the tines.
Once the soil is broke up enough to pass thru the rake, then you can start moveing the rocks to the surface with the tines and bunching them for more easy removal.
You also might search this forum for "screen filter". There are several posts about ones members have built to filter soil. Basically a mesh screen at a 45 degree angle that you dump material onto near the top with the loader. As the material tumbles down the screen, soil falls thru, rocks and debris continue to tumble and drop off the end. This would get the smaller rocks that the rake will not.
Good Luck
. Used with gauge wheels and "floating" the 3PH it will act like a road grader and help move the high spots into the low ones without digging in too deeply. A landscape rake with equal tine spacing(1.25" tine. 1.25" space) will capture just aboput everything the tiller brought up, down to about 1.25" If run at an angle, it should windrow rocks even a bit smaller than that depending on the speed that it is pulled.
