To get started means to begin something, a task, a job, an adventure, to start writing a book whatever.
"You will get started" is not about the now or future tense. (today and yesterday)
Tomorrow I will get started on finishing the decoration(decoarting the home)
It's time I got started = it's time you began or restarted something you were doing either today or previously.
I get started is not very natural. Except for situations when describing a habit.
I get started every morning very early before 8am.
It does not have to be about present or past tense. It describes when you began/stated something. It could be anytime and it could also be today which is not strictly the past tense, (yesterday as per grammar books) .
This is confusing for leaners when English use the past to refer to any time in the past it could be only minutes before, but we use the past tense the same as for yesterday.
This is something that is rarely explained well in many books.