if, by some chance, the temp of my subbed sample were out of range, would I have been informed immediately and asked for a new sample?
That is correct. And the re-submit would be conducted under direct observation, under DHHS regulations.

I'm not familiar with the eScreen/eCup test, and from what I read the results are basically same-day...so why did the lady tell me 24-48 hours?
Perhaps the "lady" has other clients in which she has to report their DT results to.