Yeah, the Ondura roofing IS asphalt, just in a different form factor than the standard "mineral surface asphalt shingles". I don't think it has the "minerals" which is tiny gravel stuck to the shingle, which presents a problem of dealing with the loose particles(with some asphalt too) when collecting water. The Ondura has a color coating? which might be paint? I'm not sure how much this reduces the leaching of asphalt into the runoff... it might take less rainfall to "wash" the dirt and bird
poop off than standard asphalt shingles...
Since you already have the roof, you might try tasting some water? If it doesn't taste good, you aren't likely to want to drink it... then I'd consider a water test on some collected water, before drinking a lot of it, and make sure they are testing for the asphalt, not just bacteria, or heavy metals, etc... You might be able to filter out something, if you know what's in there.
There might even be seasonal changes if your roof is in the sun, there might be more "flavor" in the summer? So, maybe a good time to test to see the highest levels?
You might be able to paint the roof with something less toxic (still asphalt under there) or cover it with something like
greenhouse film (UV stable plastic, not sure how much safer?)