Progress towards Helicarrier is simple, look at all the Avengers inserts. Once they are all lit, the Loki lock lights will cycle indicating the next shot to Hawkeye will start Helicarrier.
However, as mentioned earlier in this thread, if you are in Tessaract mode, the shot is disabled OR if the next Hawkeye shot will start his vs mode, that takes priority, which neither should IMO. If you have qualified Helicarrier, shooting Hawkeye should take priority over Tessaract and starting the vs mode.
You can avoid this by waiting for Tessaract mode to time out but there is no way to avoid starting Hawkeye's vs mode.