During initial climb after departure from St Pete-Clearwater International Airport (PIE), St. Petersburg, Florida, the flight attendants (FA) notified the flight crew of an odor they described as that of "burning rubber". The flight returned to PIE where two Aircraft Rescue and Firefighting (ARFF) vehicles responded and met the airplane as it stopped on the taxiway after landing. The captain communicated with ARFF personnel over Air Traffic Control (ATC) ground control frequency. According to statements, the ARFF Lieutenant advised that there was smoke coming from the #1 engine and requested that the crew shut down the engine so they could examine the airplane. The firefighter in ARFF vehicle 3 stated that while the Lieutenant was outside the vehicle examining the airplane, the flight crew reported their intent to evacuate the airplane and the firefighter advised the crew to hold off on the evacuation while he contacted the Lieutenant. According to flight crew statements, the crew asked for verification of this request three times without hearing a response. Flight crew statements indicated the flight deck crew did not communicate with the cabin crew during this time to assess the conditions in the cabin. The crew stated that they believed the delay in receiving response to their radio calls indicated ARFF personnel were busy addressing a safety concern and after hearing no further transmissions, the crew completed the evacuation checklist and advised passengers and cabin crew to proceed with evacuation. During the evacuation, one passenger sustained a serious injury (fractured wrist) and six passengers and one cabin crew member received minor injuries. Although ARFF and the flight deck crew established a direct line of communication, they lacked prompt, clear, and concise communication. Following this event, Allegiant Air implemented a Captain Leadership training program and established joint flight deck and cabin crew resource management training.