getting notifications about updates only in the “core” page

I run a few WP sites and keep track of updates on a daily basis.
Normally, I go into the Plugins page and check if there are updates to the installed plugins accordingly.
Lately, I’ve found out that even though this page doesn’t show new updates, when I go into the “/wp-admin/update-core.php” page, suddenly there are updates and from now one, the Plugins page will show these updates too. It looks like the “core” page triggers a true check for updates and only then, the admin recognizes these updates and shows them normally, as described here.

Why is that?? Am I missing something here? What can I check and how can I get the admin behavior back to its “normal” state?

I should mention that I’m not sure when this started to happen like that, as I doscovered that by mistake when working on something else…

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