How to prevent separation/layers in panna cotta?
It sounds to me like you didn't get the gelatin dispersed properly.

Since the recipe you linked to doesn't explicitly mention it, and neither does your question, I'm going to assume that you didn't bloom the gelatin first.  You must do this if you want proper dispersion of any gelatin product.

To bloom powdered gelatin, just sprinkle it over cold liquid and leave it (cold) until it's visibly swelled. This usually takes about 5 minutes.  Then simply heat and stir (thoroughly) to disperse.

To bloom sheet gelatin, you do almost the same thing - soak them for a little longer (up to 10 minutes) in cold water a separate vessel, then squeeze them to wring out any excess water, and then add to your cooking liquid (in this case cream).

You might also consider use a stick blender/immersion blender to make sure that it is completely dispersed after melting. This is usually unnecessary for gelatin, but if you're blooming it and still can't get uniform distribution, that will help.

I'm certain that if you follow the proper preparation, your panna cotta will turn out fine next time.

P.S. Do be careful not to add too much lime or other acid; gelatin will not set properly at pH levels around or below 4.