The bacteria in the biospira will very quickly attach to a hard surface and start multiplying there. Depending on a wide rage of variables the length of time it takes for them to multiply to the levels neccesarry to handle your bioload could take more then 24 hours, maybe even a day or two.
The bacteria that come in biospira will not live in the water column very long, so they quickly attach and start growing on every surface they come in contact with (like in your filter).
I presume the source where you got the biospira it came refrigerated and you kept it refrigerated from the time of purchase until you added it to your tank?