Thank you three for the interesting responses, Anne it is very interesting to hear this happened someplace else. While we did not get snow, we are generally affected by fronts that affect northern North America, just without the extremes. I looked under a couple of other junipers, one also fenced off and a couple of others which are not, and they didn't have thousands of babies, but just a few. Maybe each juniper tree has a supercycle, a year every so often where they are more fertile than usual?
I forgot to take my phone up with me when I checked this particular tree this weekend, I usually go there every Sunday. But I did snap a photo of some of the wildlings, which were taken to the community nursery and are under shade.
The dirt was half dirt they were dug up with and half not, so that could be the problem. Also maybe too much water as their still wild siblings are not currently receiving any water except dew.
I think we will try to dig up some others for transplanting once it starts raining in June, I doubt we could move them later than that as I have tried to dig up small junipers before and they very quickly form a strong deep root.
Micheal, we do have several nurseries but they tend to ignore the trees that grow naturally in this region as unfortunately, most people consider them "useless" and instead want a lime tree or something with flowers.