That’s correct...
The Commander in Chief can and has used the military for operations that do NOT meet the “act of war” declaration.
The reason for this: Can you imagine what it would be for the president to get permission from Congress before acting if action was required immediately???
I’m not agreeing with Kaine but I do believe that Congress should declare war when we are going to commit troops or carry out an an offensive act against a country that is not in the process of threatening the USA. The Constitution is not just a piece of paper and Congress needs to do their job of oversight.