Yes it is a problem. Restic does not handle it and you can end up with not consistent backup.
This is user responsibility to ensure that files are not changing during backup. The easiest way is to backup filesystem snapshots instead of live filesystem. Either VSS on Windows, APFS snapshot on macOS or BTRFS/ZFS snapshots on other systems.
You can find on Internet or even this forum multiple examples how to achieve it e.g.:
Restic is not a full backup solution taking care of any aspect of backup process. It is fantastic program but requires a bit of extra effort to implement some bits and pieces like file system snapshots. Given that it is cross platform tool it would be rather difficult to cover all possible OS and file systems quirks.