How to stop subs as TEC? A good question!
Not sure it has a good answer. Theoretically, the light frigate is supposed to counter support cruisers. Thing is, the subverter can and will shut down light frigates. Still, building masses of them, keeping them spread out if possible, and researching OVERLOAD REACTOR (or whatever the ability is called) might be one of TECs best tries. This approach would still be hard to pull off though, especially with the prevalence of the lrm-type frigate (assailants for vasari).
I think I'd try to go with a very strikecraft-heavy fleet. Micro the strikecraft to target and kill subverters (the strikecraft are immune to subverters, of course). I believe fighters are best for this, although oddly enough, the subverter might have heavy armor?
The Dunov EMP shockwave will drain subverter antimatter (not sure if it interrupts though). Thing is though, it's relatively short-ranged, and with the number of subs a vasari will be deploying, it's probably not a good option.
The Akkan's ion bolt will interrupt a subverter and stop its distortion field (shutdown ability). Thing is, what are you supposed to do, micro the ion bolt to hit every subverter that jumps? You gonna have the range for that, the antimatter, the cooldowns? Good luck trying it, LOL.
I guess that's about all the suggestions I have. Perhaps tell your friend to try fighting in the shadow of his own starbases (which are immune to subs), and within clusters of his own mine fields?