Neither is correct. Generally when complexity is specified in the standard, it's with respect to a specific operation. In this case the standard specifies that it's the number of calls to the constructor of T that must be constant, which means that push_back and push_front can not copy or move its elements.

There is never a way to guarantee that the physical amount of time is bounded by O(1) in the worst case. You could always have pathological scenarios or data structures written so that performing a move or copy of a single T could require O(n^n) time for all anyone knows.