It’s really up to you as to how you keep track of it. Since the vehicle in your example already has a face up disruption marker you really don’t have to have 2 on that vehicle, unless it helps you to remember that one is from a “Headshot” and will not be removed at the beginning of the next casualty phase (the end of the current turn).
Headshot:
“…This counter isn’t removed at the beginning of the next casualty phase.”
[Headshot occurs in step D or E below]
Turn sequence:
…
D. First player’s assault phase
E. Second player’s assault phaseÂ
F. Casualty phase (both players) [this is the beginning of the next casualty phase… in the same turn]
So, you begin the next turn. If that same vehicle should receive any hits that cause disruption then you would want to put down a face-down disruption marker. Because, after both Assault phases occur the casualty phase begins and all face-up disruption markers are removed (including the sniper one from the previous turn). Now the one that is face down for that vehicle is flipped over.
I think I understand this rule correctly. Hope that helps. If not, I sure someone else will pop in with the correct ruling.