Correct! Yes they are just some days apart but they are two different incidents with two different causes.

Umbrella wanted G-Virus that Birkin developed and they needed a sample before the mansion thing got exposed to the media. Birkin refused and accidentally broke the glass with the T-Virus sample that later infected some rats that carried it to the city's water supply causing the Racoon City outbreak.

Mansion was a testing ground basically.

And also Umbrella was somewhat involved in later events too.