After 30 seconds in cold climate, the exhaust brake engages to aid in warm up.

Sounds like your truck is doing exactly what it's supposed to do.

If you live in a climate that necessitates the block heater being plugged in, I'd suggest plugging your truck in.

Hell I used to plug my 4th Gen in at night here in Arizona during the winter just so I wouldn't have to wait for it to warm up in the morning before work & so the exhaust brake wouldn't engage in my HOA Nazi neighborhood.