The trailer brake is supposed to pop slightly before the tractor, so you can maintain control. If they are not popping out all the way something is wrong.
Fanning down more would not affect the trailer brakes because they are locked and the psi is already too low to keep the spring engaged.
I had never heard of "compounding the brakes" until I read your question, so this is based on a few minutes of googling it. But what I found is that in older equipment, you could cause damage by applying the service brakes when the parking brakes hadn't been released. But newer equipment has an "anti-compounding valve" which is supposed to avoid this problem. Also, even without that it seems like you would be OK as long as you didn't step hard on the brakes.
So, sorry to hear about that. How did the rest of the test go? Did he have you stop immediately then, or did you go through the rest of pre-trip?
When you fail air brakes you can’t move on
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Today I took my air brake test. I failed when fanning down between 40-20. My trailer brake button popped out the tractor brake button popped out 1/2 way. I got through the build up phase and completed it. I told the examiner I was now going to secure my truck and get my chocks. I opened the door and he said do me a favor pull on your yellow button. It popped out completely then. He said he thought I would catch it during my 85-100 test. I know I failed because the truck wasn’t secure. If I had pulled the button out when I secured my truck would I have failed then?
Then my second question, if they don’t pop out at the same time, and I continue to fan down my brakes until the tractor button pops, aren’t I compounding the trailer brakes when I continue to fan down?