Ah, I missed that reply that came in while I was composing mine about adding the URLs.
Great news! Thanks for taking the time to post an update.
Arduino IDE does need to download the package index file from the URL you added to your preferences before Boards Manager will list the platforms from the new index. So if you open Boards Manager and do a search before the index download is finished, the search results won't include those platforms. Maybe that was the cause.
OK, there is a known bug in Arduino IDE that affects the installation of ATTinyCore (and the other DrAzzy/SpenceKonde platforms) specifically (but not the Digistump platforms). If you have trouble, you can find instructions here:
I'll be happy to provide assistance with that if you end up running into trouble.