"not what the tutorials say, by the way"
this is because the example in the tutorial does not have the form action submitting to another page.
"but how do I validate the entire form?"
In the server validation wizard, select the validation type, click the lightning bolt next to server variable, select the form element to validate, click the plus button to add it to the list of validations to perform.
then repeat, select the next validation type, click the lightning bolt, select he next form element, click the plus button again.
repeat until all validations have been added.