How long does it take to get sick?

My daughter spent the day with her cousin at their grandmothers house on Tuesday. They were kissing, hugging and playing with each other all day. When my sister in law picked my niece up, she had a 101 fever that went unnoticed during the day. I was told that my niece had some congestion that morning that they thought were allergies. Anyway, I’ve prepared for my daughter to get sick, but she’s been acting fine. My niece still has the fever and congestion. Her fever got to 103.5 last night. I’m thinking it may be roseola, but will need to wait until the fever breaks. Anyway, about how many days after she was exposed to an illness should I rest easy? How long does it usually take to get sick?