Why do I get arrested by stormcloaks whenever I kill imperials escorting stormcloak prisoners? I mean the stormcloak city/hold guards.

Killing* in title.

I'm not sure but perhaps you should let them attack you first.

I have experience on this but it's from a glitch. My Jarl Balgruuf of Whiterun didn't want to go out of the palace, even though there were Stormcloaks everywhere congratulating me on victory. So while I "waited" (in vain) for him to gather everything up and leave I decided to roam around the palace.

While doing so I encountered Balgruuf's wife and kids in one of the rooms. She greeted me "can't a woman have her privacy? Go away!" or something similar.

Barely did I have the chance to turn around to leave. Suddenly I found a couple of stormcloak soldiers attacking me!

As I ran out of the palace and out in the town of Whiterun, ALL the stormcloaks started attacking me and my bounty in Whiterun started increasing by the thousands (wtf?!?)

Nice thanks they gave me for winning them the town...