If I had of been there then I would have concluded immediately that there were more casualties than me by myself - therefore I needed assistance, that I couldn't actually get to those casualties myself without incurring potential danger to myself - therefore I needed specialist assistance. That takes less than a second to come to the conclusion.
It took the ambulance service 6 mins to come to that conclusion. It took 10 mins for the park to dial 999 but in that time first aiders on site had to get to the ride and make sure it was safe for them to enter to start assessing the situation. If the initial assessment had taken longer maybe someone would have realised to request the fire service also during the initial 999 call.