I use the same 2 stroke oil for all my machines, and haven't had any issues so far.
One thing that I did see though was that the 2 stroke mixing bottles are useless. I have had 2 different ones, and found that they had 2 problems- firstly that it is difficult to gauge the correct levels using the markings, and secondly (and more serious) that the measurements were massively incorrect. One of the bottles was so bad that, on subsequent investigation it was found to be giving mixes of around 25:1 instead of the required 40:1.
Instead now I use a plastic 25ml measuring spoon, fill the petrol container with exactly 4 or 5 litres, then put 4 or 5 spoonfulls of oil into it. Much more exact mix.