The jump box likely doesn't put out the same voltage as the alternator, and may have back-feed prevention circuitry. I would guess that instruction saying to disconnect within 30 seconds of starting the vehicle is either because:
1. There is no back-feed prevention circuitry
2. They don't want to risk a failed diode to prevent back-feed from the alternator to the pack, over-charging of the pack, and the potential explosion of the jump pack battery (li-ion)
Leaving your jump-pack installed in parallel with the battery was a very foolish thing to do, regardless. Even if the reason is due to a failed alternator, these packs are NOT meant to run the vehicle. While the amperage draw is much lower running than starting the engine, I still wouldn't trust the pack to do that, with the battery OUT OF the loop.
Finally, if the jump-pack wasn't hot, discharged or exploded, then it likely has nothing to do with your starter battery issue.
What you SHOULD do, on a go-forward basis, is spend the $15 (or less) to get a multimeter. You can even buy a cheap lighter-socket plug-in that will display voltage. Why in the world would you guess that the alternator might not be up to snuff when you can spend seconds checking it???
p.s. I would immediately check what the alternator is putting out and check the voltage of the battery before driving that vehicle anywhere!!!