I think the problem comes because you're mixing READING and EDITING screens. If you're editing, you need to make it very clear. Your action buttons (please do not confuse with CTA) make sense on an edition page, but of course, they're not needed if the user is viewing data.
This is why you're facing this problem: in one screen you have nothing to save, because you're mixing different types of views.
As for your most general question, tabs MAY have different CTAs, as long as they hold completely different content. This is more common on mobile, and quite unusual on desktop. You may think of them as just carousels with CTAs if you want.
However, in your specific case, you don't have CTAs. In this case, you shouldn't use action buttons on one tab and nothing on another. As a matter of fact, you shouldn't use tabs at all! Tabs hide snippets of information from the user, so you'll end with incomplete journeys and/or lots of errors
From Tabs, user right:
Use tabs only when users don't need to see content from multiple tabs
simultaneously. If people do need to compare the info behind different
tabs, then having to switch back and forth puts an added burden on
their short-term memory, increases cognitive load and interaction
cost, and lowers usability compared to a design that puts everything
on one big page.
Of course, there are many way to do what you want to do in a more seamless way, but that's another question.