Hiring a cheaper person to do a job nobody has documented reproduces the problem in another timezone. Training against your actual process is the part that makes it work.
An agency sends you a CV. This includes documenting the process first and training against it, so the person arrives able to do your version of the job.
Agreed before placement. Most arrangements guarantee a fixed overlap window with your working day rather than leaving it to chance.
Replacement terms are in the contract before anyone starts.