OK then, I will answer to myself (and possibly to those who’s looking for the same problem).
I’ve tried newest WPBakery Page Builder 5.5.4 with no luck.
I’ve also tried code from this thread Tabs without plugin https://codepen.io/anon/pen/NObqRO with no success.
Also, plugin Squelch Tabs and Accordions Shortcodes doesn’t work well with Illdy template.
Finally, a plugin which goes well with Illdy 2.1.1 I found is Tabby Responsive Tabs currently in Version: 1.2.3
It is quite lightweight, but anyone can code own CSS code or buy an add-on.
Anyway, thanks for your time.
Cheers Michal
(not Michael)