How does a dog get roundworms in only one month?

I am very familiar with tape worms and how they are transmitted and what they look like, etc. I have a question about roundworms, though.
My pup was has been thoroughly wormed several times before I bought her, and she had a fecal come back negative right before I got her. The vet gave her a Sentinal pill last month as heartworm and flea preventative. She had no reaction or dead worms in her stool last month. THIS month they gave her the same pill and the next day I found dead roundworms in her stool. I took a stool sample in, just to be sure, but I know they were round worms, not tape worms.

Where can a dog get roundworms? And can they mature in only one month? I was concerned that it was from the raw meat she gets, but the vet tech said that they can't get round worms from raw meat. She said they can get other things, but not round worms.

I am worried that she picked them up on our walks? Or what if she ate the neighbors cat poop?

Anyway, if any of you have experience with this, I'd love to know! Thanks ....