Speaking for myself, the perception of time hasn't really changed through technology. The need for ever greater precision has though.

As we travel farther and faster, we enter new frames of reference. Our most familiar use of time is in reference to our Earth the solar system we’re in. When we leave the planet we need to travel much faster and we are gone for extended periods.

Time is an expression of motion. While on Earth, only our own motion, relative to an apparently still Earth, is meaningful to us. To travel to other planets and beyond we must concern ourselves with the motion of many other objects. It’s like driving without traffic lights, regulations, or any other controls. You have to study the other objects before you leave, chose your route well, and time things perfectly.