Before I go on, I should mention it would be helpful to put a written description in your OP. The video is a bit confusing/scattered.
Anyway, I believe I have a similar problem. Whenever I use Siri, my alert sounds go to full volume. For instance, I typically will lock the phone out of habit, and the "click" will knock you over. I can clear the problem by tapping on the alert sound slider in Settings > General > Sound. I have the option to "change with buttons" off, though it doesn't seem to make a difference.
There's at least one other situation that triggers the problem, but I can't remember what it was - if I get it to repeat, I'll post back.
The Siri related problem is very repeatable, though.
+1 on writing a description of your problem. Im not clicking on the link but it sounds like your sound is loud when Siri comes up? Use the volume buttons while Siri is up to turn it down.