The reason the compatibility page shows a blank is that Joomla! 3.5 itself is not tested with PHP 7.1 and 7.2 since it predates these versions of PHP. We have never included Joomla/PHP combinations which have not been supported by the Joomla! project in our Compatibility page.
To answer your question, Admin Tools 5.1.4 and Akeeba Backup 6.2.1 do support Joomla! 3.5 in general and PHP 7.1 in general. So yes, they should work on your site as long as Joomla! itself does not seem to break with the unsupported by Joomla version of PHP you chose to run Joomla on. That is to say, yes, OUR software works, but JOOMLA ITSELF might not.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
Please keep in mind my timezone and cultural differences when reading my replies. Thank you!