That would support the theory that it was an incorrect out time that many CBS stations hubbed master controls went with, and was not cut off on the actual network feed.
Most likely so, and master control times were not adjusted for the end of prime time for the affected stations.
As is common with streaming services, the Paramount feed will have a significant delay from OTA. I have YouTube TV, and the local stations on it are about 25 seconds behind OTA.
You have to remember that most station master controls are hubbed elsewhere, perhaps more than a thousand miles away, and those hubs are running dozens, if not hundreds of program feeds at the same time. The local stations have nothing to do with that within their own buildings. The days of stations having their own in-house master control are mostly gone.