I've had mine for a few years, so it's not "NEW" but I suspect it is essentially the same as you describe.
The mounts are clear; I tried scanning a page, but it didn't work very well because apparently you can't scan clear

You can sort of see it in this photo ...

The mounts are attached to the page only along the top edge. The bottom half of the mount is not attached at all so you can lift the bottom half, insert your stamp upside-down gum facing you (as shown in the photo). When you release it looks great.
I've never had a mount come off the page and I've never had a stamp fall out of the mount.
All of the mounts in Volume 1 have a 'horizontal' split (like the one in the photo). In the later volumes, with some of the souvenir sheets, the slit is 'vertical' -- it helps prevent the sheets from bending when you turn the pages. Even with the vertical slit, I've never had one fall out of the mount.
My only caveat is more relevant to modern stamps than early one --- as with any pre-cut mount, if you have a stamp with selvage, it's not going to fit perfectly.
Kirk