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Which e-commerce plugin are you using? WooCommerce?
If the button performs an Ajax request or submits a form when you click on it, then you’re correct that Query Monitor won’t show you the queries and other information that occurred during that processing. It will only show you the information for the page load after it happened and you were presumably redirected back to the order page.
I know this is frustrating and I have a solution in the works but there’s no ETA yet. It’s quite a lot of work.
If your MySQL server has query logging enabled you may be able to use that to see which queries are running during that request, it’s just a bit fiddly to dig through those logs.