Some devices have evil task killer services integrated that interfere with the Telegram notification service. For the notifications to work, you need to add Telegram to allowed apps in those devices' security settings. Task killers normally force apps running in the background to quit, removing them from memory. However, Android can intelligently manage processes on its own – it doesn't need a task killer
See bottom “Battery Saving and Cache Cleaning Tools” on this page for some screenshots of known battery “saving” apps.