Hi Kat,
It really depends on each individual plant on how long it takes for the bud to bloom. I don't find dips versus tets takes longer or less time, it just depends on the plant. Usually tetraploids have larger sized blooms (depending on if you have older or newer ones) and the bud will continue to grow until the size it needs to be before it opens.
I have some buds that I thought were going to be another week or so before blooming and 2 days later they opened and I have others that I think are going to open the next day that take a week.
Also, some buds have color to them almost the whole time they are a bud. For example, Buddy's Victoria Jade has purple buds and I have another (can't remember name) that has red buds. They are green to begin with but once they get a little bigger they get their color.
The one petal opening could be because it came loose too soon (maybe you touched or bumped it). If you are still having cooler weather then it may be slower opening. Some daylilies don't mind the coolness and will open up while others it may slow them down.
Here's a photo of one that isn't ready to open for a few more days but it got bumped (rather manhandled) and popped the bud tip open.
Hope this makes since and helps some.
Do you have a photo of it you could post?