Wyeast smack pack question

I tried my first Wyeast smack pack with a starter and I'm not sure of the results. I tried to locate the inner packet and I thought I gave it several good whacks but was unable to determine if I had actually broken it. I waited maybe 2 hours and saw no swelling. I continued with the starter and poured in the yeast.

The inner packet looked like it had possibly two joined packets, or it was one packet sealed in half with a lot of extra plastic. The inner packet did not break, so I cut it and dumped it in the starter. I wasn't around after this and did not see it actively ferment, but after a day and a half it looked to have a good bit of yeast sediment at the bottom.

Did I do the right thing? Is there any reason it's not safe to use this yeast?

Thanks.

The inner packet is just a little bit of wort that is intended to wake the yeast up a little and make the pack swell so you know the yeast are alive and kicking.

The inner pack also contains a little bit of yeast nutrient, so ideally it should get into the starter. Not the end of the world if it doesn't. It's interesting, this is the second (recent) thread that mentions a double-sealed inner pack.

Your starter should be fine.