I've never had any problems with the tinsel but I've had the tree almost over several times from various kittens in my life! They all love playing with the baubles.
If you are out make sure the cats can't get anywhere near the tree and it should be ok.
The last Siamese kitten I had liked to bite the presents too - she liked nibbling paper!
I'll have my new kitten this year and I can't wait to see how she behaves with the tree.