Yeah, I have noticed that straight away, and it made me read an article on Wikipedia about Southern Russian dialects. Essentially there are different ways that these southern dialects are similar to both Ukrainian and Belarusian (mind you I don't know anything about Belarusian, I am just rephrasing Wikipedia here) from that generic area. Pretty interesting stuff.
It were Ukrainians who initially populated this region, so it's no wonder that people there still preserve the Ukrainian accent. People from Donetsk and Luhansk puppet republics also speak with this Ukrainian accent.
I know that Russia metodically tried to eradicate any language and accent that is not Muscovite russian. But I guess it's difficult to remove every small bit of accent