While building a villager trading area which uses powered and unpowered rails to transport the villages to their designated trading point, the villagers were moving the minecarts on their own.
I believe the same issue was reported (MC-64836) but has been marked as resolved...?
I am not sure if this is still an existing 'bug' or an issue that has returned.
I cannot upload a picture of a villager moving a minecart but I made a short video: https://youtu.be/6xLJM9DOhME
I usually play Minecraft with Optifine, but this issue still exists on full Vanilla in both creative and survival worlds.
This issue will be fixed in 1.13.