My app normally works just fine, until I face a strange problem on specific device. There are 2 activities in App. After I start ActivityB inside of ActivityA, ActivityA starts
There's an Android developer setting called "Do not keep activities". The description for this option is "Destroy every activity as soon as the user leaves it." This sounds like a good description of what you're seeing, and since you're only seeing it on a few phones the idea that this is caused by a non-default system setting seems plausible.
Ideally your app would still work in this scenario, even if less optimally. But if this setting is a problem for your app, you may wish to document this problem for your users.