It seems that most of the FP helis tend to move to the left on power up, so I would say that is normal. Just know that it will happen and compensate. Movement to the rear could be caused if your CG is off or if you heli isn't trimmed correctly. I have heard on this forum that some people have had to move some of the other components forward as well as the battery, in order to establish proper CG.

Also there is usually a piece on the battery holder(attached to the landing skids) that can be removed. This will allow the battery to be placed even further forward than the design intended. This method could fix your CG prob(if your prob is CG caused) with out having to move the reciever/mixer, etc forward. So try this method first, after rechecking your heli for proper trim.