Welcome to the Forum.
Yes, "coming off the floor" the PTO clutch engages first, GENERALLY you pause briefly while the implement spins up and the engine recovers it's revs, the drive clutch engages second.
They are not so much a "Single Dual Clutch" as they are two separate clutches performing different functions and operated by the same foot lever (pedal).
Best to start at the beginning;
Before engaging the PTO at all.
Set the lowering speed valve so that the implement lowers in about 3 seconds, no need to be precise, but generally you don't want to slam it onto/into the ground or take half a field's length for it to touch down.
OK, assuming that and everything else (ROPS, seat belt, etc.) raise the implement.
Depress clutch ALL the way, select the gear and range you will use, engage PTO, engage clutch until you hear the implement start to spin up.
Release a brake somewhere about now, rasie the loader bucket too if so equipped.
The next thing is a CHOICE, there are arguments for one way and arguments for the other way, I will present both and try to not argue it either way.
a) You MIGHT CHOOSE TO engage the clutch fully and start the tractor moving with the engine at a very low speed (idle or slightly above).
b) You MIGHT CHOOSE TO bring the engine speed up to whatever is indicated to produce the required PTO speed of 540 or 1,000 and THEN engage the tractor's drive line clutch.
Whichever way you do it is fine with me (-:
OK, so you're headed off to the field or wherever.
Get a sense of where you want the implement to start touching down, be conscious of your speed and estimate how far you travel in 3 seconds.
When you are 5 seconds away from starting your first row get into the hip dysplasia position and start watching the ground under the implement - this is what you spent all that money for, not much, eh ?
A couple of seconds later shove that position lever forwards and see what happens (-:
report back, DO report back
According to what you are pulling, your turn-around space, etc you may or may not have to stop the tractor and reverse it at the ends of rows.
Once you know where the clutches engage/disengage you will be able to do any needed 3 point turns with the PTO still engaged.
ALWAYS lift the implement (except sprayers and SOME mowers) when turning.
Maybe best to lift a mower when turning, at least initially.