Huh, I'm getting the same results with this very simple test script:

using UnityEngine;
using System.Collections;

public class InvokeTest : MonoBehaviour 
{
    void Start () 
    {
       InvokeRepeating("Tick", 0f, 1f);
    }

    void Tick()
    {
       Debug.Log(Time.timeSinceLevelLoad);
    }
}

"0" logs twice, with further logs coming in once every second.

This is the first I've heard of this issue, but I found this thread from last December, which includes a suggestion to use a very small number like 0.001 instead of 0.