Hibbard scored two of the Ospreys' six tries at the Liberty Stadium, while the Lions contingent as a whole had a huge impact on proceedings as they set the platform for backs Eli Walker (two), Jeff Hassler and Matthew Morgan to touch down in the bonus-point triumph.
"The Lions have been great for us in terms of the environment. Three of them have played key parts in the first two games in pushing us onwards, but Alun Wyn and Tips coming back to the matchday squad this week does make a difference," said Rees.
"Physically, we were able to impose ourselves and we did that for large chunks of the game. And we had to because, fair play to Edinburgh, there was a big physicality about them also. We had to man up, and the Lions were to the fore there.
"Richard Hibbard's growing and growing all the time as a player. He's as reckless as ever in terms of throwing himself around, but it does create a good mentality around the team that we want a bit of edge about the things we do. He certainly gives us that, as well as some strong set piece play. And he was obviously crowing about the tries he scored, just to put a glow on his night!"
There was plenty of glow about the evening for the Ospreys as a whole as well as they blew away an Edinburgh outfit who had beaten the Dragons at Murrayfield the previous week.
Rees had stressed the need to back up an opening week win in Treviso and last Saturday's 29-29 draw at champions Leinster and his side did just that as they had all five points wrapped up with close to half an hour remaining.
The Ospreys led 18-3 at the break and pushed on in some style in the second-half despite losing Tipuric to a tip tackle on 50 minutes. Instead of allowing Edinburgh a way back into proceedings following Tim Visser's 50th Celtic League try and Tipuric's sin binning, the hosts put the game to bed with a brace of further tries during their openside's absence.
Unsurprisingly, Rees was delighted with the clinical approach, although he refused to get carried away with a victory that moved them up to second in the standings.
"We have to be pleased. Last season there were games that slipped away in terms of pushing our advantage home, but we were quite clinical in turning pressure into points and we put the game to bed fairly early," added Rees.
"We felt there was a little bit of an untidiness about us in the first half, though, with a high turnover rate. And even though, tactically, the game seemed fairly comfortable for us, we did have a couple of poor moments defensively. There was the try and a couple of linebreaks that Edinburgh carved out, against what is normally a water-tight defence. But we kept going and, overall, it was a good evening.
"I'd certainly hope there is more to come. We want to make the Liberty a fortress - we haven't lost here for a year or so, so we've got to just keep pushing this form now."
The Ospreys are still waiting for confirmation of Smith's injury, with initial reports suggesting the hard-working blindside may have dislocated his knee.
"We've seen the doctor and he says it could go one of two ways. It's potentially a blown-out knee, or you could get lucky and it could work its way back in after being displaced," said Rees.
"But you're still talking a few weeks out, even with the best-case scenario. The worst case is if it's back to a long period of rehab for Tom, which is a shame because he had a year of that last term.
"He's been fantastic as a leader in the group over the summer. You talk about the Lions, but he's a player who seizes hold of the group. His performances over the first three games have been rock solid in a good back five for us."