Even more than that, if you are running multiple instances of the app in multiple pods concurrently, then all of those logs will be joined together.
If you mean one instance in each pod, then each should be labelled differently and you can filter down to one instance.
If you mean running multiple instances in each pod (and container?), then the standard kubectl log output will also have them all joined together. For both of those, you would need to add another unique identifier to each line, or run each instance in a separate container so you can submit the logs with the pod name and container name combined being the unique identifier.
Not being able to filter between multiple processes or multiple restart of a container was a genuine issue, not being able to filter between pods of a deployment is not.
Anyhow, the nice thing about the system is that one can get anything that is preferable as long as the logs are annotated correctly (with pod and container id).