Indeed - something often misunderstood as always recorded from the perspective of a third party observer.

Quick follow up question. If you did depart and travelled at near-ligth speed to another galaxy, arrived there in a few seconds and then looked back at the earth - would it appear as only a few seconds have passed for the earthlings back home as well?

By the same token, if you are actively watching another galaxy as you travel at near-light speed towards it - will you be watching that galaxy "age" at an extremely fast pace throughout the journey?