Pilots are advised to try an immediate (new word for 'hot') relight as soon as a flame out is diagnosed in whatever position in the flight envelope. If it fails or the engine overtemps the engine should be shutdown and a normal or cold relight should be carried out within the cleared relight envelope.
During engine testing in the nineties, I used 10 seconds from shutdown for an immediate relight test and thirty seconds from shutdown for a cold relight, so yes, we still do it that way. However, modern FADEC control normally includes an automatic immediate relight facility, so the pilot has been taken out of the immediate relight loop.