Can't speak for everywhere but we run EMT driver and EMT-P. Like changes for like. If the new crew is there and the the call is within 15 minutes of shift change, they take it. Otherwise, if the new driver is in, the old can leave. Same for the medics. Sometimes though, someone is running real late. In this case, a chief officer can ok going out of service. In the case we depend on mutual aid or one of our other stations.
PS. Small operation. 3 stations, one in each of the 3 townships we serve. One ALS unit per station is the norm.