No, the anger I feel will not 'cause' my actions, as my response will be result of much more than the current thoughts I have, it will be the result of my lifetime of experiences leading up to this moment.
This part is not determinism. It's just saying there was a cause for your choice.
And when I 'decide' something it will be the only possible decision based on all of my prior life and previous decisions.
This is the assumption of determinism. That you cannot resist the effect of any of these prior causes.
I seem to be saying that nothing is decided in the moment, that decisions are products of all our past experiences.
Well, you do make a decision. Determinism only assumes the decision that you do make was the only decision you could make in that particular situation.
Like saying the 8 ball could decide whether or not to go into the pocket regardless of how it was hit.
You however, as opposed to the 8 ball, possess knowledge and experience and the ability to control the motion, to a specific degree, of your body.
Events that happen in the past no longer exist. They no longer exert actual influence. They are now only memories, thought, ideas that you possess. You have to a greater or lesser degree, it varies with the individual, control over them.
While you can't control the event which cause you to feel anger in the first place. You can control your thoughts and desires. You can choose to think "happy" thought. Relive a happy or pleasant experience. These choices will negate the influence of anger on your actions.
Part of Buddhism is right thoughts, right action. It assume that you at least have the ability to control your thoughts. And, your thoughts control your actions.