I found proliferations on the following daylilies:
Whatchamacallit x1
Prairie Blue Eyes x2
Trahlyta x2
Ruffled Strawberry Parfait x2
Coburg Fright Wig x5
Fancy Buttons x1
Royal Cypher x1

Some are still in water growing their roots, others have already been potted up. After they have all been potted up how do you take care of them? I've been told 2 complete opposite ways for doing this. One says, water very little and put them in a cool room for the winter. They other said to water weekly and put them in a sunny window for the winter. Do they need to go dormant their first year? Will they do it naturally or what? Needless to say, I'm completely confused (again)

This is just my thoughts on the directions you have been given.
It seems the first set of directions are assuming the plants are going to go dormant naturally, so just give them a little water and keep them cool and alive and plant them as small rooted proliferations in the spring.
I think the second set of instructions are assuming you want the plants not to go dormant and to be as large and healthy as you can get them, by keeping them warm, feeding them watering them and giving them all the light you can and hoping they don't go dormant and will be much larger plants when planted in the spring.

My proliferations get the tough love treatment. I just put them in the soil, usually next to the mother plant, water them well and leave them. They have all survived. I never rooted them in water. I do this in September when I am cleaning up the spent scapes.

Maybe you can try this with one you are not too worried about.

I'm pretty sure they would not survive if I planted them outside now. There roots are barely 2 inches. Plus they are calling for a killing frost next weekend. I suppose it will be like everything else, trial and error.

To add my two cents worth--I have been growing prolifs for four years here. The first year, my experiment was to plant some outside and some kept inside in a window for the winter. The ones outside all died while the ones inside were thriving, planted out in the spring and are now blooming plants. Now, the prolifs I want to keep are put in water to grow the roots, then potted up and grown on in the south window. Sometimes I need to pot on mid winter as roots grow out the bottom but not often.

Edited to add--I forgot to mention that I usually have poor snow cover with half a dozen freeze/thaw cycles a winter. These are murder on several cultivars.

I guess I have been lucky, or the proliferations were from tough plants. If I get a proliferation on a plant that is very special, I will baby it and try the indoor treatment. So far, the proliferations have only been on big clumps, so I am not worried about their survival.

I took a photo today of last year's proliferation from Heavenly Blues and the one from this year that I just stuck in beside last year's a few days ago. We will see if it makes it through the winter this year or if I was just lucky last year.

I also did this with a prolif from Prairie Blues eyes and one from Star Child, but that was a few years ago and they just look like another fan now.

I have a proliferation from Matthew Weldon that I pulled inside yesterday. It will stay a container with water until the roots have gown out a bit, then I will plant outside. But it's still in the 90's in my zone...record highs for this time of year. No chance of frost any time soon. My weather pattern is different than yours so what works for me may not work for you.

Valerie, do you get a good snow cover for winter where you live?

I saw a proliferation with a bloom on it the other day. Is that common? Should have went back and took a picture.

For what it is worth, I usually get some roots to show up by putting the prolif in some water in a sunny spot on a window sill. Once I see some roots, I place it in the ground next to the mother plant. I have had more success doing that than babying it by potting it up. They tend to rot away when I pot them up.

David

The large proliferation in the photo I posted yesterday had a bloom on it last summer, when it was a proliferation attached to a scape. The prolif on Prairie Blue Eyes also bloomed, so it does happen

@RobinSeeds
Yes, I get very good snow cover where I am.

Some years we get good snow cover that sticks around most of the winter. I've found the snow to be good insulation and prevents the destructive and harmful (to the plants) freeze and thaw cycle. When we have ranging winter temps without the snow cover, I lose plants, especially young ones.

I put the prolif in a cup or pot of growing medium and place it in a container with an inch of water to water it from the bottom. (same as I do seeds started outdoors before cold weather). It usually has good roots in a couple of weeks. The only reason I don't put them directly in the ground like Valerie, is due the the late summer heat when the prolif is needing harvested. 90f + temps are not favorable to start them directly in the ground unless it is in shade with regular water.
It is not uncommon for me to see some of the prolifs bloom on the mother plant. I had one plant with a prolif on each scape and all bloomed on the mother plant.

Here is a picture of one of my Galaxy Explosion seedlings.
This prolif had 5 blooms and was typical of multiple prolifs on this plant.

It could be that I have success with direct planting for several reasons. I take them off the plant in September when the weather has cooled, and we start receiving good rainfall. Also, we get good snow cover, so do not face freeze/thaw cycles.

rainfall is good too!

Prolifs that bloom...amazing kidfishing!

It will be interesting to see if my prolifs make it or not. Another 'live and learn' experience with daylilies.