"Time" not a dimension.

[Zen Badger]

I mean subjective inasmuch as the effects of time dilation only apply to the person in question.

Not to time itself.

Which person is meaningfully in question, and how does the subjectivity effect this, when clocks on satellites are measured and found systemically and predicatably slower than identical clocks on the ground?

Untutored intuition about time gained through direct animal senses far too dull to detect relativistic effects is worth almost as little as the bible or koran in clarifying the basic properties of time and space.

Generally time dilation effects are illustrated using people.

The effects are the same regardless of whether you use a person or a clock.(or particles for that matter)

My point being that the effects could be explained not by time slowing down but the process's of the subject or object in question slowing down.

Remembering that one of the results of travelling at light speed is gaining infinite mass, that is sure to slow you down.