There's a connection to the on-going conflict. Poroshenko has a lot of financial interests in Russia. While he's not pro-Russian, strictly speaking, he has been avoiding doing anything that would jeopardize his interests there. A lot of people blame his weak response for Crimean occupation and the ongoing civil war.
On the other hand, Saakashvili was president of Georgia during Russian invasion of that country. He's mega-pissed at Russian gov't and almost as pissed about some Ukrainian politicians doing little about Russian aggression. Consequently, he's very open about his criticism of certain individuals in Ukrainian gov't, and he gets a lot of popular support out of that. There's growing sentiment in Ukraine that revolution didn't change a whole lot in who runs the country and how.
Consequently, no, I don't see this doing anything to increase the tensions in the Eastern Ukraine, and yes, this is certainly an internal matter, but it can be, in many ways, seen as fallout from the military aggression that the Eastern region has been a subject to.
Na if Saakashvili would run for presiden he could get something about 3 to 5%, so much about his popularity and now he´s in jail, so not seeng how he can influence the military crysis.