Holy crap, that's no good

I'm glad you're both okay.
I don't do agility, but I was under the fairy tale impression that it was one dog at a time, in one ring, and that having something like parallel courses would instigate something like...well, this.
In the lower level classes we start working the dogs on leash with the room divided so they get used to other dogs and people being out and running around a little, the noise of the equipment, dogs barking (I swear to God every Sheltie at my club barks non-stop while they train - I welcome an ice pick in my temple).
The idea is that while on leash you can work with them and desensitize them to the high distraction, intensely active environment. It's great for working on focus for agility. This is the first real problem I've encountered or witnessed.
But, yeah. Still you've got dogs running and working in pretty high drive and some of them that are fairly high strung can be harder to direct/re-direct than others.
Oh man, what a bummer! That sounds so scary for both of you! How is Tali doing? I hope it won't have a lasting negative impact for her. And I hope you are ok too!
I currently take privates so am not faced with this situation. The drawback is that there are not the same level of distractions we'll face at trials down the road. Where I trained in NJ it was foundation classes and we were all in one large room, with sections of the room dedicated to certain equipment/activities. Many dogs were still on leash so the risk of a dog taking off was pretty low.
I will be interested to hear other inputs though. I'm so sorry you and Tali had to experience that and hope it never happens again!
Tali is fine.

My heart was in my throat and I was visibly shaking when the adrenaline started wearing off a few minutes later. LOL But Tali was basically unfazed.
The Dal literally plowed right through the fence, taking all of it crashing down, and he charged her, coming up right behind me, while she was on the dog walk. She jumped off (thankfully it wasn't full height), tucked her nub and ran away from him. He was so fast, I barely realized what was happening before he was nearly on top of her. He cornered her against the chute and, silly girl, she play bowed at first but he lunged forward and snapped in her face.
She spun around and tried to run from him again when he did that and he leapt forward again after her rear, mouth open. I was hauling @ss to get to her - they had made it across the room from me and the trainers at this point. All I could see was Tali's little left leg extended out as she was pushing to take off running and his mouth open wide with these huge teeth going right for that little leg. His mouth seemed enormous in that moment.
I barely got to her in time and slammed my right leg down right in front of his face and in between them. I don't know how he missed biting me. I heard his teeth clap together as he jumped when he hit my leg. It gave Tali just enough time to make it about 5-feet away and 2 trainers made it to us and were on top of him while he was trying to scramble around me. I finally had a chance to run to her and grab her.
She was fine. LOL She was running away so I grabbed her by her rear and she spun around to me and immediately sat while I took her by the collar. I was just holding on to anything on her that I could, making sure she was firmly in my grasp. She didn't struggle at all though. She just sat there. LOL So I praised her heavily and gave her some treats. I had her do some little things to redirect us both - shake, down, sit, a little bouncy heeling, lots and lots of praise and happy voice.
The Dal was put up and the trainers wanted to end on a good note for Tali (she's been nervous about the dog walk some so it was just our luck he came steamrolling down on her while she was on the dog walk). So we ran thru the chute a few times - she loves the chute and it's always a party for her. And then we approached the dog walk and she blew my mind. She did it with ease and made her contacts perfectly several times in a row so we ended with that.
She's a good, stable, easy going girl. She literally didn't miss a beat. My heart was in my throat the rest of the night though. I just kept replaying his mouth coming so close to her leg in my head all night and thinking of how bad it could have been. Tali won't start a fight and she sure won't raise a dog that challenges her, but if he'd have gotten ahold of her she'd have defended herself. It was scary but we got super lucky that's all it was.
I get shaky retelling it. I'm just so relieved and thankful she's okay physically and that it really didn't bother her at all. It scared the bejesus out of me though. I would have been devestated had anything happened to her.
That had to have been scary. Perhaps if they could come up with a divider/fence that was higher than a dog could jump. Also make everyone sitting around ringside watching have their dogs on leashes.
There was an incident at Dream Park a couple of months ago. A dog in one ring was running his course at the same time in the next ring a dog was running. At one point one dog left his ring and ran into the adjoining ring and joined the other dog in a tandem A-frame exhibition.
That's one problem with our dividing fence - it's not a true barrier. It's open fencing so the dogs can see through it and it stands with weights keeping the poles upright so it can be knocked over with relative ease by a decent size dog. The height isn't bad, but the dogs don't have to clear it - they can (apparently) plow through it.
Any dog that's not on the floor working is required to be crated ringside. So that helps prevent problems should a dog leave their ring and just go ringside.
Oh wow, how frightening! All of our previous training was done with only 1 dog in the ring at a time (except beginners... we were all in the ring but dogs were leashed).
I'm now doing privates, which is nice. We start a group class in May at a new training center, and all dogs are in the ring but only 1 runs at a time typically.
The class I'm in now with Fiona runs one ring, one dog at a time and that's helpful but it's more advanced than Tali's class and there are fewer dogs in it. The class Tali is in is one that usually weeds people out. They try it and then drop agility after because they're not progressing or they don't enjoy it, so I think the 2 rings is somewhat because of class size and somewhat an attempt to desensitize the dogs to working with another ring in progress next to them.
Poor tali and you! How scary, this is why I like solid and appropriate height divider panels between rings if there are to be two+ rings whether a trial or just class. The building we train at has approx. 5-6 ft solid panels to split the huge space into 2 rings. They can't see each other, nor jump over them.
I especially love it right now because if another dog barks, mabel can't see them so it's easier to regain her focus and train her on distractions.
Here's the panels in a video
ThinkPawsitiveDog - YouTube
Thanks for the video link! I'm going to forward the panel suggestion to the agility chair at my club. Something like that would be sooooo helpful.