You're right that the present perfect continuous started in the past and is continuing, but what makes that tense special is more of an emphasis on the duration or continuous course of the action. Both tenses are used to express that an action began in the past and is still going on or has just finished.
The present perfect simple tends to stand out as mainly being used to express that an action is completed or to emphasise the result.
But "to be" in this tense followed by an adjective or a state (not a verb gerund like "watching", but "happy" or "on holiday", for instance) is a special case and can only exist in this form because the key verb is "to be". It would be incorrect to say:
*He has been being...
This means that whether the action is continuing to the present moment or not, depends on the context or the implications that the verb allows. So, I can say:
I've been at work since 6AM.
And this implies that I am still at work right now.
But then again,
I've been worried sick about you!
doesn't imply that right this second I'm worried because I'm talking to the person and know they are safe. This tense is used because my worry started in the past, and continued up to the very recent present, but actually stopped just a moment ago.
For your example, "involving" yourself in something isn't the kind of thing you start and stop, but more of an ongoing state (depending heavily on the context though), so even if right this second he isn't doing something that means he is actively involved (like maybe he's eating or sleeping right now), he is still in general involved right now.