I looks like we are talking about different things.
So you have a team (i suppose could be just 1) or teams across few time zones.
Each team should deploy in a way that they have people ready to fix thing if they go bad.
You can do that by having large enough team in similar timezomes (+/- 2-3 hr), or by paying extra for having people on standby at 1am.
My personal opinion is that having large enough team (again could just be 1 guy) in similar time zone is preferable.
Bottom line is, deploying new stuff is always risky. That's why people spend so much time trying to reduce this risk (various test, CI, staged rollout ...). And sometimes all of that still fails, and you need people to either rollback or fix it on the spot.
[1] As always there are exceptions to this rule