‘But Snape tried to kill me!’
‘No, no, no. I tried to kill you. Your friend Miss Granger accidentally knocked me over as she rushed to set fire to Snape at that Quidditch match. She broke my eye contact with you. Another few seconds and I’d have got you off that broom. I’d have managed it before then if Snape hadn’t been muttering a countercurse, trying to save you.’
Philosopher's Stone - page 209 - Bloomsbury - chapter seventeen, The Man With Two Faces - Harry Potter and Professor Quirrell
Since Snape is a good guy, it's safe to assume that he didn't see Quirrell performing a curse on Harry. Otherwise, he would have reported it to Dumbledore.
Also, since no other wizard there was applying a countercurse to save Harry, it is clear that nobody suspected that Harry was under an evil curse. So the curse wasn't like Wi-Fi. Since Snape performed a countercurse, not a normal saving spell, he needed to know about the curse in the first place. How did he know about it?