Very little of the infection actually spread from the mansion. Traces of the virus leaked into the sewer from the mansion (the mansion, hospital and laboratories are all connected via the sewer system, which is in turn connected to the underground carrying-out tunnels) and infected a few people within the vicinity, but the infection wouldn't have spread. The cause of the zombies which appeared in August came from the leak caused by Birkin at the abandoned plant, and these ones began to spread very slowly. It was the attack on Birkin on September 23 that caused a huge leak and was ultimately responsible for the city's destruction, which was made worse by the fact that most of Raccoon City was in one place at the time: the stadium. It became a zombie domino effect at that point.
The mutant strain is however purchased from Umbrella and used by Javier to create the faster and stronger "Javier Zombies" in Darkside Chronicles. These weren't true Crimson Heads apparently since their state of suspended animation was artificially induced. Actually receiving damage seems to make the mutation more aggressive, which makes sense since the V-ACT process reconstructs tissue.
EDIT: Of course I'm talking from the perspective of a new game based in Raccoon City, rather than a remake. It could work in the latter but good luck trying get even remotely the same quality as the BH1 remake. The time for remakes of any of the older games has long since passed and nothing good will come out of remaking them now.