I would have handled it in a completely different way. I would have first noticed the incident. Turned around if I was in ear shot of the woman and informed her that was not a "safe" move and you could have hurt yourself as well as informing her that you do not wish to see her get hurt before starting their day at the park.
Whatever she says after that it in regards to being rude is just mute for me. If she apologizes and thanks you, then say "you're welcome". You've said your piece. Most likely you 2 would have started a conversation about the parks and have moved in a positive direction versus a heated exchange.
At the end of the ride I would have then told the CM what I witnessed and for him/her to please be aware of people jumping on the tram while in motion as it is unsafe as the CM should know or I'm assuming was taught before they started operating the vehicle.
In the end both people were wrong to take it to a dramatic temper level. It ruins your day to some degree, especially if you're going into the same park with that person and thus seeing them again by chance. If moments like this let you get yourself to a dramatic yelling level then maybe you need to not say anything at all. You're not helping by yelling and you're not helping by going back and forth with someone who is being unreasonable.