We are have a roof put on and it is raining...it is secure for the roof to shingle contained by the precipitation?
Answers: No. The roofer I know won't put shingles on in the rainfall.
If the roofer wants to do it, I'd stop them. Not simply are there safekeeping & liability issues, but putting shingles on top of damp underlayment traps moisture. Trapped moisture causes mold and wood rot & the roof won't second as long.