Also other mods I have activated are:
R.E.D modpack
Strange Religions
Promotions Expansions Pack
Chaos Civilization
Faster Aircraft Animations

Please note that this combination of mods have worked before with Barbarians evolved but suddenly doesn't which makes it even more weird.

I tested out some things and I found out that the city you have chosen to be "liberated" when capturing a barbarian city is the one getting destroyed on the first turn for some reason.

That's a feature the mod (or more accurately, a workaround).

When you are playing with the Barbarian civ, there are actually two civs in play:
1. The Barbarian civilization
2. The tribal Barbarians (the ones that spawn in camps)

Barbarian cities are created as tribal, then "captured" by Barbarians, so that the player has the option of "liberating" the city. Liberating it doesn't make it yours - it returns it to the tribes. Then it disperses on the next turn, because having two barbarian groups holding cities is confusing.

This feature came about because people wanted a way to "liberate" a Barbarian city. Capturing them actually makes other Civilizations hate you (you look like a warmonger). Liberating them makes you a hero. The downside is, you can't keep a liberated Barbarian city. If I had to give a practical in-game explanation for that, it's that Barbarian cities lack the infrastructure to maintain themselves once liberated from barbarism. Technically, it's because you don't want to have cities on the game map owned by the civilization and the tribal guys at the same time.

If you don't care about liberating cities, you can simply play without the Barbarian civilization. In this case the tribal Barbarians will step up and found cities, but they will not be able to be Liberated - capture and raze will be your only options and you will be viewed as a warmonger.

Originally posted by Neronic/Maxmad:

I tested out some things and I found out that the city you have chosen to be "liberated" when capturing a barbarian city is the one getting destroyed on the first turn for some reason.

I also experience this when testing the game. It seems that only because of enabling city to be "liberated" will cause this issue.

Interesting. Thanks for the report.