FFF,
You could argue your job at the time was just what you did: supervise your student.
He was even more surprised that I hadn't noticed a large puddle of oil under his aircraft and informed ATC that he had a problem.
Don't know about you, but when I am starting an engine (or supervising a student doing it) I don't tend to spend my time looking at puddles under other aircraft. I am looking for anybody coming near me and any signs there is something wrong with MY engine. If I happen to spot something with another aircraft I'd report it, but it is not my main task at the time.
Don't think you did anything 'wrong' here. And those drops might well have been water: oil on your windscreen (even clean oil) looks quite different and, specially if if there is some moisture around as well at the time, can have a very interesting optical effect.
Cheers
Gerard