We have the same problem. We put down landscaping cloth and then straw...which is now full of weeds.
In pulling up the weeds, I noticed the roots were attached to the top of the landscaping cloth, not coming up from under it.
What has probably happened is that wind and birds scatter seeds that germinate. You will either have to pull/dig them up or spray them. There is nothing you can do to prevent this except put out preemergence in about February! Or several times a year if you are in a climate with a continual growing season!
Just strong hardy weed, mine has just done this after a year. I have pulled up the mat and spray roundup on the weeds and grass staying away for my plants. Then put down new weed mat and put the bark back on top.
Nothing is wrong. It's just that weed seeds get scattered by the wind, birds, animals and in other ways. They are able to take root in very little dirt. That's why it's very hard to get rid of weeds. All you can do is keep taking them out. You can use full strength vinegar or boiling water to kill any currently showing but they will come back eventually. It's just an on going process unless you clean everything out that use a pre-emergent like Preen. Even that isn't 100% successful. Be sure to follow the instructions on the label. Wishing you the best.