If we're talking about the one relay module PER siding method, this requires a DELAY-OFF module. As mentioned previously, some of the relay modules online are not-as-described.
Above show some modules that will work. The more expensive multi-function timers can perform more tricks. The two on top require a one-time "programming" to select the mode to Delay-off and to set the timing parameters. The one on the bottom "only" performs the delay-off function and you simply turn the adjustment control to set the delay time; one of my earlier posts shows an ebay listing and I'd think the item description would be the same if you prefer Amazon or similar US distributor.
As I understand it, you may have some delay modules (that use the NE555 IC chip) but they are NOT of the Delay-OFF type. As is often the case, there are ways to hack them to change functionality but really not worth the effort when you can get exactly what you want for just a couple bucks.
