There's nothing wrong with using commas. In American English classes they teach you to stay away from comma splices and try to use other punctuation, but sometimes other punctuation just ruins what you're trying to say.
I've noticed that English writers sometimes to whole single sentence paragraphs using commas...it can be a little disorienting at times, but as long as you aren't going on and on and on, comma splices are fine.
This sentence is fine, however there is always room for improvement: "Whenever he was alone this is how he passed the time, meditating, thinking of the past, and of the future, not just his own, but of his people, the Jaffa."
Try: "Whenever he was alone, this is how he passed the time: meditating, thinking of the past and of the future—not just his own, but of his people; the Jaffa."