Common usage in English after: It's time [that] [etc.]
It's time he left for work. It's time you went to bed**.
It's time we shut up. [ha ha, invariable]
It's time Little Johnny did his homework.
What pattern emerges?
The pattern is that the phrase is commonly followed by a second clause (a relative clause) but not really a protasis (dependent clause), as what comes after the phrase can stand on it own and is comprised of a subject + simple past + [the rest of the clause].
So, returning to the question:
- It's [high] time he faced up to something.
It follows the pattern perfectly. And there is no subjunctive heffalump in sight.
(I am sure there are more go-getting grammarians who might want to give this a go. :))
And without pursuing this too far, it is worth mentioning that other dummy-type phrases such as: It's silly, It's funny, It's nonsense, also are followed by a simple past in the second clause.
- It's silly [that] he insisted on that.
- It's nonsense [that] he left us in the dark.
- It's tragic[that] they went on that hike.
That brings us to the fact that a dummy subject followed by adjectives in the predicate or even some nouns can follow this pattern.