In your example, a refers first to "a", and then to "ty". You're not mutating any String instance; you're just changing which String instance a refers to. For example, this:
String a = "a";
String b = a; // b refers to the same String as a
a = "b"; // a now refers to a different instance
System.out.println(b);
prints "a", because we never mutate the String instance that b points to.
