When using matches(), you are asking if the string you provided matches your regex as a whole. It is as if you added ^ at the beginning of your regex and $ at the end.

Your regex is otherwise fine, and returns what you expect. I recommend testing it regexplanet.com, Java mode. You will see when matches() is true, when it false, and what each find() will return.

To solve your problem, I think you only need to remove the if (matcher.matches()) condition.

You should use String.matches() method :

System.out.println("My_File_Name.txt".matches("\\w+\\.\\w+"));

You can also use java.util.regex package.

java.util.regex.Pattern pattern = 
java.util.regex.Pattern.compile("\\w+\\.\\w+");

java.util.regex.Matcher matcher = pattern.matcher("My_File_Name.txt");

System.out.println(matcher.matches());

For more information about REGEX and JAVA, look at this page : https://docs.oracle.com/javase/7/docs/api/java/util/regex/Pattern.html

After testing on both [regex101 and RegExr] my test cases are detected properly

That seems unlikely, since your pattern is indeed faulty, not only in Java's Regex dialect but also in the ones tested by those sites. The only plausible explanation I see is that you were not actually testing the cases you think you were. For example, your test inputs may have had trailing spaces or newlines.

Which brings me to the problem with your pattern. As you already observe,

Now the intersting part is is when I remove [^.] it will detect,

That's because that sub-expression matches a character (different from .). Your overall pattern therefore indeed does not match "gruell-Core.exe" because there is no character after the .exe. Try matching "gruell-Core.exee" instead.

If you want your matches to end with .exe, then anchor your pattern instead: gruell.*\.exe$