- Yes that's the reason why it doesn't sound right, because you're not using the HP & LP filters during the sidechain.
Looking deeper into this, I'm not sure you'll be able to replicate the same behavior with Live's Auto FIlter :
Basically there's 2 filters running at the same time inside Volcano 2, a High Pass & a Low Pass filter, they are used in LR ( stereo mode ) and they are "linked", so controlling one parameter like the filter resonance will be equally reflected on both HP & LP filters.
Here's the macro Routing for Volcano 2 :
Now the problem is that you can't use 2 filters at the same time in one instance of Live's Auto Filter, you will need to use 2 instances in your effect rack and could automate the On/OFF, Frequency Filter and Resonance for each one, but I don't think you'll get the same result since those 2 instances will be processed in series ( from left to right ) and not really linked.
So it won't give the same results, I'm not sure about an alternative to Volcano 2, there's a lot of filter plugins out there, even free ones, but don't know about one with this L/R linked mode.
That's as far as I can go with this one I think, have you been through all the videos yet ? Because I'm surprised it's not explained better. Also, keep in mind that many times you won't always be able to replicate the exact same workflow as the tutors, just because you won't have the same plugins doesn't mean that there's nothing to learn about it. What's important to get from tutorials is what the tutor tried to achieve and you might find the method interesting or not and come up with another solution as well, which is also a very good way to learn. Of course, you could decide to purchase the missing plugin, but let's be honest, if you choose that road, it's no good for the budget and it's also not the best way to progress IMHO.
Hope that was helpful anyway 
Cheers !