If you get them in wrong don't worry - they won't work... LOL That little #4 part will not work right if it is in backwards. It is good that you figured it out. The tension disks do not spoon - they go curved sides together so the thread has somewhere to go (I have seen some tensions are kind of flat and have a raised part in the center - I'm thinking Singer 401 and others - they are the same on both sides)
Not all of the posts just screw out. Some have a set screw - you may see another set screw that holds the tension holder thingy in the machine. The set screw can be on either side or on top. I have learned to take a bit of time looking it over. Springs can vary, too. They all have to spring back. They can not bind or dangle. That manual is the only place I've seen that tells how to do it. The pin inside the tension stud needs to have the flat end outward. Some tension pins are straight with out a little nail head or a flat spot
My sister is here from Arizona - she's been wanting to learn something about tensions. We did tension 101 this evening. I have a really filthy old Singer 66. We took it apart - she did the clean up on the tension parts. It was coated in dried up oil and lint. Some oil cleans off with rubbing alcohol and some needs nail polish remover - we are girls..... we use what we have... besides it smells better than lacquer thinner... get the kind that is 100%. This one needed lacquer thinner. We got outside parts cleaned and decided to pull the rest out and clean it. It was a good thing we did. That pin was all gooey. The Singer 66 had a set pin on the right so we took that off - full of goo and lint. Then there was a set screw on the back of the piece. That released the pin - we also cleaned the tension hole. The shellac flaked off the machine. We will have to look up Glenn's fix it for the finish tomorrow if we have time. While she was cleaning that I was cleaning other parts - everything was gross. The bobbin winder mechanism is covered in rust - everything else had a very protective coating of goo - dried on oil. Then we got to the bobbin area. It was so full of lint it barely moved. We dug out lint for a long time. I had trouble getting the bobbin race out - we dug out lots of lint and then got the bobbin race out - more lint under it. I think this was the most lint I have ever seen. Then I oiled and oiled and oiled. There is either a wee bit of gummed up oil somewhere or some rust somewhere.
I showed my sister how to set the tension. She did a good job and we only had to re do it once when we found a part we missed. Since the wiring is cracked and missing, I'm thinking I want to put a hand crank on that machine and run it and oil it until it goes smooth - also give the tension a road test. We haven't tried it with thread in it yet. That bobbin area may still need a little more clean up. It looks like it needs a new oil wick. It seems like the tension and the bobbin areas are usually the most difficult to get right. I also cleaned up the balance wheel - it had a LOT of dried goo in that area. My sister's comment was you don't want to be in any kind of a hurry... I wonder where she learned that.