How organize and thest this code?

I have a conceptual doubt about how to organize and test a code like the following, where a call to an auxiliar method is the first instruction of all the public methods of the class. My idea is make the code clean and testable.

The code is an example to try to illustrate this by a class "cache". This class has an option prefix will be applied to all keys in the cache if it is setted.

import java.util.HashMap;


public class Cache {
    private HashMap<String, Integer> inMemoryCache;
    private String prefix;


    public Cache() {
        this.inMemoryCache = new HashMap<String, Integer>();
        prefix = null;
    }

    public void setPrefix(String prefix) {
        this.prefix = prefix;
    }

    public int getValue(String key) throws NullPointerException {
        String prefixedKey = applyPrefixOrDefault(key);
        return inMemoryCache.get(prefixedKey);
    }

    public void setValue(String key, int value) {
        String prefixedKey = applyPrefixOrDefault(key);
        inMemoryCache.put(prefixedKey, value);
    }

    public boolean isCached(String key) {
        String prefixedKey = applyPrefixOrDefault(key);
        return inMemoryCache.containsKey(prefixedKey);
    }

    private String applyPrefixOrDefault(String key) {
        if (prefix == null) {
            return key;
        } else {
            return prefix + key;
        }
    }


    public static void main (String[] arg) {
        Cache cache = new Cache();
        cache.setPrefix("global:");
        cache.setValue("id", 4);
        int value = cache.getValue("id");
        System.out.println(value);
    }
}

This code poses two questions to me:

1. If I had many methods accessing the inner hash table, would it be right separate the behavior of the cache in one class and the behavior of the prefix in other?

2. What would be the cleanest way to test this? Test the getValue, setValue and isCached is simple if we do not consider the prefix. With the prefix we need test two thing, the correct internal behavior of the cache and we need test also that all methods call applyPrefixOrDefault before accessing the data.

This is a common use case and I'm sure there must be some design pattern to organize this. Any idea?