You’ve mentioned both e-ticket and mobile ticket - these aren’t the same thing. The Trainline website explains here how and when to activate a mobile ticket:
https://www.thetrainline.com/en/help/question/4500/how-do-i-downloadactivate-my-mobile-tickets
This includes (sorry can’t see how to make it a proper quote):
Download ticket
You can then Download ticket to view the actual ticket on your device which includes an image of the barcode that will be scanned at the station. You can only download your Mobile Ticket to one device, so make sure you download it to whichever device you’re planning to take with you when you travel.
Activate ticket
You will need to activate your downloaded ticket before travelling, however this should only be done on the day of travel and once you are sure you will be travelling that day. Activating your ticket is irreversible, once it’s been activated it cannot be changed, refunded or moved so we recommend you only activate it just before boarding. Tickets should not be activated before 04.30 am on the day of travel, unless your train leaves before then.
Move ticket
If you’ve already downloaded the ticket but now are travelling with a different device then you can move it.
Open our app in the device you’d like to move your tickets to. Log in to your trainline account and then download your tickets to your new device. Just so you know, before you travel you need to activate the ticket on your device. However, once activated you can no longer move, change, or refund the ticket so it's best to wait until just before travel before activating.