setTimeout and setInterval
Describe your problem better

While this may seem not be a thing to be pointing out in a code review it is important to describe your problem in a nice way.
I would describe it as follows:

I want to yield each property of an object every three seconds. However the first one should be delayed by 10 seconds.

Separation of concerns

You are mixing the time repeating problem with the property yielding. 
You also don't allow a way to specify a different strategy for what to do whenever another property comes (in this case that would be the console.log).

function setIntervalDelayed(delay, interval, cb){
    setTimeout(function(){
        if(cb()){
            setIntervalDelayed(interval, interval, cb);
        }
    }, delay);
}

function yieldProperties(obj, delay, interval, cb){
    var props = Object.getOwnPropertyNames(obj);
    setIntervalDelayed(delay, interval, function(){
        if(props.length == 0) return false;
        cb(obj[props[0]]);
        props.shift();
        return props.length &gt; 0;
    })  
}

yieldProperties({x:0, y:1, z:2}, 1000 * 10, 1000 * 3, console.log);


EDIT

While my approach is sligthly better then yours there is still mixed code. Again yieldProperties is doing more then it should, it still has that depedency of the delay and interval arguments, that don't really fit there.
Solution: implement iterator pattern.

    function setIntervalDelayed(delay, interval, cb){
        setTimeout(function(){
            if(cb()){
                setIntervalDelayed(interval, interval, cb);
            }
        }, delay);
    }

    function iterate(arr, cb){
        var i = 0;
        return function(){
            if(i &gt;= arr.length) return false;
            cb.apply(arr[i]);
            ++i;
            return true;
        };
    }

    function yieldProperties(obj, cb){
        return iterate(Object.getOwnPropertyNames(obj), function(){
            cb({
                name: this.toString(),
                value: obj[this]
            });
        });
    }

    setIntervalDelayed(10 * 1000, 3 * 1000, yieldProperties({x:0, y:1, z:2}, console.log.bind(console)))