In USA, how is Vother Verified Paper Audit Trail in voting systems implemented? In particular, how is the secrecy of votes insured?

I note that it would be compromised if bulletins where sequentially printed on a continuous roll of paper, or it bulletins where cut but somewhat stacked in order, or the machine opened during the voting process with one record (or few) in the VVPAT. Independently, there's the risk of compromise by the printing process (thru noise if mechanical, or electromagnetic emission).

Context: I'm French, and have never seen VVPAT operating (our few voting machines have been designed in the previous century, and use an electronic record of individual votes, which makes it impossible for a voter to verify it). Link to a video showing a common USA system operating would be great.