Yeah, that's definitely not right. And just to double-check, you've given that group Viewing and Edit restrictions on that specific page? Hopefully it's as easy as that.
But, my gut tells me that you're running into an inherited permissions issue. Basically, there's a parent page to the page that you've set restrictions on that has tighter access restrictions, which are cascading down and (essentially) overwriting the restrictions you're setting on the group.
(You can read more about inherited restrictions, among other things, here.)
The first step I'd take is see if there are any parent pages that have restrictions set, and if so, make sure the group you're trying to add restrictions to are also included in those parent pages.
Oh, another thing to check is to make sure that the group you're trying to restrict has access to the Space as well. Space permissions override everything else, so if the group doesn't have any access to the Space, the restrictions you're setting won't have any effect.
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