Spotter Network will report directly to the SN server so reports can be seen by SN users. Upon reporting, it also tries to send the report to the NWS, but not all offices are equipped to receive data that way. Most offices either will have E-Spotter online or just another version of online reporting available. If not, the easiest way is to call your NWS directly and speak to the forecaster in charge.
For those offices that do have either E-Spotter or regular online reporting active, your report will pop up on the forecaster's screen almost immediately.