You have hit a Joomla bug.
When you update from Admin Tools Core to Professional what should happen is Joomla removes the old update site (Admin Tools Core) and installs the new one (Admin Tools Professional) in its place. If that fails the next update you will see will be Admin Tools Core. Installing the Core package — which is what Joomla's extensions updater does — will replace Pro with Core.
The solution is to unpublish the Admin Tools Core update site from Joomla's Extensions, Manage, Update Sites page; download Admin Tools Professional from our site; install the Pro ZIP file twice in a row, without uninstalling it before or in between (this addresses another bug in Joomla's extensions installer...). Then go to Components, Admin Tools, Options and make sure your Download ID is correct.
Nicholas K. Dionysopoulos
Lead Developer and Director
🇬🇷Greek: native 🇬🇧English: excellent 🇫🇷French: basic • 🕐 My time zone is Europe / Athens
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