Commanding the Red Army's Sherman Tanks by Dmitriy Ioza is an autobiographical account by a Soviet tanker that alongside retelling some battle accounts, also goes into some of the logistics/training background and Lend Lease.
Also even though it's not a book, here is an interview with that author done by the Russian government, for memorialising purposes. There are more interviews on there with Soviet soldiers from most branches of the military as well, the website has a nice collection.
Rereading that interview now, here's a nice excerpt of how his brigade treating civilians. Who knows how much is embellishments after 40 years, but I don't see why the main gist woud not be true:
So, you didn't have hatred for these enemy soldiers, did you?
No, of course not. We understood that they were also human beings.
What about your relationships with the civilian population?
When the 2nd Ukrainian Front reached the Romanian border in March 1944 we stopped, and remained in place until August. In accordance with wartime laws, the entire civilian population had to be removed from the front-line zone to a depth of 100 kilometers. These people had already planted their field gardens. The authorities announced the evacuation to the population over the radio and sent out transportation to pick them up the next morning. With tears in their eyes these Moldavians shook their heads. How could this be? They had to abandon their fields! What would be left upon their return?
So the evacuation went ahead as required, and we had practically no contact with the civilian population. At the time I was chief of staff for ammunition supply for the battalion. The brigade commander summoned me and said, "Loza, are you from peasant stock?" I replied in the affirmative. "Well, I thought so. I'm appointing you as team chief! You will be responsible for weeding these gardens and ensuring that everything grows and so on. And God forbid that even one cucumber is spoiled! Don't touch anything! If necessary, plant your own crops."
Teams were organized; in my brigade we had 25 men. All spring and summer long we fussed over these field gardens. In the fall, when the troops departed, we were told to invite a kolkhoz chairman as a representative, and we formally signed over to him all these field and kitchen gardens. When the housewife returned to the home where I myself was living, she immediately ran out to her garden and was dumbfounded. There she saw enormous pumpkins, tomatoes, and melons. She returned to the house on the run, fell at my feet, and began to kiss my boots. "Dear son! We thought that everything would be dried up and beat down. But it turns out that we have everything, and all we have to do is gather it in!" This is an example of how we related to our populace.