“That should do it” is commonly said just after a small action has been completed. It means “that will probably be enough” or “that is likely to solve the problem”, not “that object ought to perform another action”. After tightening a loose connection, for example: “I’ve tightened the connection. That should do it.”
Should here does not express duty. It gives a confident prediction with a little room for uncertainty: the speaker expects success, but the result has not been fully tested. The expression is entirely natural in everyday Australian English. If completion is already confirmed, “That’s done” is more definite. “That’ll do” can instead mean that something is merely sufficient, and may carry the tone of “that is enough”.
https://www.ldoceonline.com/dictionary/that-should-do-it
https://www.merriam-webster.com/dictionary/that%20will%2Fshould%20do%20it
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