She's the type [to be precise] about everything

I've known for years that she's the type to be precise about everything.

I know to-infinitive refers to the current time, not a future time when it qualifies the superlative degree or an ordinal number, but my example is not the case. And I think "to be precise" here means "which will be precise."

So I was wondering why it is "type to be precise," not "type precise."