Not much is known about
this phenomenon, especially since most of the coverage of these events are
glossed/ skipped over. On the other hand, there are some things that I can potentially
clarify and shed light on.

First, let’s go over
some examples.

America: 

We get a brief – albeit shallow
–depiction of America’s Civil War in chapter 211 of World Stars. No insight is
given, other than the fact that America is visibly distressed [x].

Spain: 

We get two strips that
cover Spain’s Civil War.

One involves Romano
getting mad at Spain for not participating in WW2. Romano had fought in the Spanish
Civil War and got shot in the butt during the conflict. Meanwhile, Spain is too
poor to give a significant contribution to the war effort [x].

Another strip involves
Romano calling Spain after he and Veneziano were taken as prisoners of war by
England. Spain explains that he can’t bail the two out because he was too busy
making roses. This seems to occur at the end of the Spanish
Civil War [x].

Russia: 

We get a brief look at
Russia’s title change from Russia to the USSR in this panel here. It’s from one of
the first original webcomics [x].

Unpacking this information:

It’s a common headcanon
that during civil wars, a separate personification develops. For example, the
US Confederates would have developed their own personification.

While this hasn’t been
shown, rules in canon can potentially support this.

In chapter 1 of World
Stars, it’s stated that personifications can exist for as little as a few days
to several centuries – or millennia if you consider the Ancients, China, Japan,
and Turkey [x].

There’s also the
hypothetical example where Canada dreams of Quebec becoming an actual country [x]. What’s important is that the new nation is born after the secession is
legally recognized, thus differentiating the situation from the American Civil
War.

Something that’s always
puzzled me about this scene is its ambiguity. When Canada states “anything but
Montreal” it could easily be interpreted as Montreal – as a municipal personification
– evolving to represent Quebec as a nation. Given that states and Japanese
prefectures are personified, it’s not far-fetched for a city to be personified
as well. We just haven’t seen this yet in canon.

On the other hand, we
also know from the above panel that personifications can change their personalities
as a result of a title change. 

In that case, when two gov’ts fight for power in
a civil war, there isn’t a need for a second personification except in the case
where two legitimate states form. The end result is that if a new gov’t assumes
power and changes the name of the country, the personification can undergo a
personality change.

That said, since very little information is known about civil wars in Hetalia, it’s difficult to draw anything conclusive about them.