Hi bushymcbush
Gosh, I'm sorry to hear you feel your DD has got off to a bit of a shaky start.
I think the teacher is trying to 'stamp her authority' from the get go here and there is a mindset that if you start off very firm, you nip problems in the bud and get the expected good behavior you desire.
To be fair to the teacher 30 four year olds can be a handful and I certainly don't think I'd be able to manage that easily.
I think you also may be suffering a bit from the change from how things were at nursery. Every little bump and milestone seemed to be reported whilst my DDs were at nursery and primary school and it was an overwhelmingly happy, cuddly, friendly place. Primary school can seem very impersonal and stern in comparison. Certainly DD1 had a very stern Year R teacher, who I found pretty shockingly cold in the first weeks (we weren't even allowed to go in and help them hang up coats, etc... and kiss them goodbye) but ultimately DD1 absolutely adored this teacher.
I wouldn't get too wound up that your DD moved slightly down the 'star chart'. It's good that the teacher is monitoring behavior (hopefully of all students) and oddly enough at that age getting a sticker or smiley face on the board is a big deal.
It's very early days. Talk to your DD about why she didn't do what the teacher asked, but don't make a big deal about it. Just try and discover if the problem was one of not understanding what to do or how to do it - or if your DD was just being a bit difficult. If the latter, then try to support the teacher by explaining that sometimes at school you do have to pack up and put away when the teacher asks you to so you can get on to the next lesson, go to assembly, go home, go to lunch, etc... The school day goes very quickly and if children don't cooperate, it just eats into the fun time you can have learning, doing and playing.
HTH