Ping sensor showing wrong status

that’s because you’ve got the indentations wrong. trigger:, condition: and action: should have the same level (also, if you only have 1 item under those blocks, you dont need the list notation:

- id: '1598685272140'
  alias: Abc Comes Home
  description: ''
  trigger:
    platform: state
    entity_id: device_tracker.abc
    to: home
  condition:
    - condition: template
      value_template: >
        {{trigger.to_state is not none and
	      trigger.from_state is not none and
		  trigger.to_state.state != trigger.from_state.state}}
    - condition: template
	  value_template: >
	    {{(now() - trigger.from_state.last_changed).total_seconds() >
					 states('input_number.presence_timer')|int}}  
	- condition: template     
	  value_template: >
	    {{trigger.to_state.state == 'home'}}
  action:
    service: persistent_notification.create
    data:
      message: Arrived Home
      title: Abc

Marius
Thank you so much - looks like its working now, although as no-one has left the house yet I still have to wait and see whether it gives me a true positive. At least it has stopped all the false positives so far.
Really appreciate your patience with me
Mike