The author put "(assuming these four cards represent the rest of the deck):" in the problem. So you have to assume that the rules followed by these four cards do, in fact, represent the entire deck.
But there are different sets of rules that could govern the information that you glean from the four cards. The simplest rule could be that all the cards have been given random assignments. The four cards would still represent the rest of the deck. All kinds of rule sets could be represented in any four cards as long as you only get to see four cards. We are have one given, "these four cards represent the rest of the deck" but at no time are we told that if "If a vowel is printed on one side of the card, then an even number is printed on the other side" than the deck must all be arranged such that ALL cards with a vowel must have an even number. There are other assignments that could hold true. I'm sure they meant it to mean that you can confirm that all cards with a vowel must have an even number which can be confirmed by turning up two cards but if you are putting up a logic puzzle than you should state you givens in a super hard way. The second I see this kind of thing I get a the same frightened feeling that I got taking structured logic exams. Leave out a given that seems obvious and you fail the problem. If you turned up an even without a vowel you could toss this shit out but if you turned up even's with vowels you still can't confirm the rule.
I've read this question about 20 times now and I guess I'm just not reading it with good will. This is the kind of thing that teachers would hit us with in logic classes. If you take the premise that "these four cards represent the rest of the deck" means that numbers with vowels are even and you confirm it by turning up just two cards and there is no other assignment of vowels to numbers even or oddness that can exist such that this rule isn't true. There are assignments of numbers and eveness that could hold for four cards such that cards with even numbers will have vowels but not hold true for the rest of the deck. It would in no way invalidate the premiss that "these four cards represent the rest of the deck" and still not make it true that all cards with even numbers have vowels on the other side.
I understand what you mean now. I think the test is a bit more basic than what you're looking for and sort of falls into its own little "box" of rules. It's more designed as a quick "gotcha" than a deep, winding path of logic, IMO.