yes rarely, very rarely, you can love someone after one day, time makes no differene to love, it can however change how you percieve a person over time so love can fade in and out of a relationship sometimes somewhat randomly as the way someone behaves can have a deep effect upon your perception of them in terms of rmantic association. With regards to the other lady, you are naturally assuming she has the same social and moral values as you do, which is that fidelity is top of her agenda, when she may have entirely different values and not really care that much if her boyfriend enjoys himself elsewhere occasionally.
Everyone is different, but a word of advice, this does not sound healthy for you, as it's clearly distressing you, so probably best if you take these good people's advice and tell him to sling his hook unless he can commit to you solely.