How do I limit a website?

Websites are handled a little differently from apps, because of how Apple's picker works.

Open the website in Safari first (type the address in the bar and let the page load — tapping a search result won't work). Once you've visited it, open Choose in Precursor and search for the address under the picker's "Other" section to select it. There is no place to type a web address directly; the site has to have been visited in Safari first to show up. Apps and websites are limited separately.