Pig Latin game resolved with a regex in Java
Your code looks fine. I would write this with a different approach. It is up to you, which is better.

public static String pigLatin(String word) {
    Pattern firstVowelPattern = Pattern.compile("^([aeiouAEIOU])");
    Matcher matcher = firstVowelPattern.matcher(word);
    if (matcher.find()) return word + "way";
    return word.replaceAll("^([^aeiouAEIOU]*)(.+)", "$2$1ay");
}


I do not use any arrays and splitting a string, but I solve it with more regex expressions.  The key element of this solution is how replaceAll works. In the first parameter, I pass two regex expression and in second parameter I switch results of them using $2$1.

As you can see I did not use if-else statement, only if. In your solution else also is redundant.