My understanding of the way the reservoir works is hot coolant expanding flows from the radiator to the reservoir, which acts as a storage tank. Then as the coolant cools (contracts), radiator vacuum pulls water from the reservoir back into the radiator. By your filling the reservoir when it's cold, as hot coolant comes from the radiator to the reservoir, the reservoir then overflows onto the ground.
The reservoir should be low when cold, and the radiator should be about 1" from full when cold. You don't want to remove the cap when the radiator is hot, as the coolant is under pressure at that time and will blow out all over anything nearby (like you).
Start checking the radiator when cool, and advise. Don't pay any attention to the reservoir.
So if "Have tractor will travel" is correct, then the system is operating as intended.
I like his explanation. It covers all of the OP's original facts, then gives a logical explanation for what is happening, and means that the system is operating as intended. It working that way does depend on the reservoir having an airtight pickup tube that extends down somewhere to or below the bottom half of the reservoir. But most have that.
If it has that tube, I can't resist adding a little more detail to expand "Have Tractor's good advice.
After running the tractor and you shut it off and everything starts to cool down, the fluid in that reservoir will be drawn back into the radiator until one of two things happen.
1. the radiator will suck back fluid until it's radiator vacuum is equal to the air pressure, or .....
2. the radiator will suck back fluid until the fluid level in the reservoir falls below inlet to the pickup tube in the reservoir.
Either one of those things happening will stop the flow back into the radiator. And both are basically good. So when everything is cooled off the next morning make a mark on the reservoir at what ever level that fluid is at, and also take off the radiator cap to check that the fluid in the radiator is at the proper level (about an inch or so down from the cap).
If it is right in the radiator, put the cap on & don't add any more fluid to that reservoir. If it isn't high enough in the radiator or you are uncertain... it won't hurt to add fluid to the radiator.. but NOT to the reservoir. If you had to add fluid to the radiator, expect it may overflow while working but hang in there..... the fluid in the reservoir will go ahead and level itself out by a day later.
After reading through all this anyone can ask questions if they want. But to me it is sounding like the OP's JD950 is working right. I'd say it sounds like it has been getting rid of the unneeded extra coolant and then coming back to proper level the next morning.
And thanks to "Have Tractor will Travel" for his insight.
rScotty