The way you're matched with teammates/enemies actually hasn't really changed at all. It's still based on your rating. However, the name has changed from ELO to hidden MMR (Match-making rating) and it's no longer a visible number.
You are always matched with players of a similar MMR. However, since, unlike ELO, this rating is not visible, you can't necessarily see that when you check other players on Lolking. What's more is your MMR doesn't necessarily match up exactly with what division/tier you're in, especially if you've been winning or losing a lot lately.
Example: You get placed into Bronze 1 and start winning 80% of your games, but you lose 45promotion series in a row. Your hidden MMR is probably close to Silver 3 level, but the series requirement is holding you back. you will be matched with Silver 3 and 4 players.
Example 2: You get placed into Gold 5 and promptly lose 23 games in a row. Your MMR is now closer to Silver 3 level, but you can't drop to silver tier unless you go inactive. You will be matched with Silver 3 players.
I'm surprised you're seeing players over a tier away from you, but I suppose they must be huge outliers in terms of MMR. It could be because those players are in a duo queue with players in a much lower division, like Gold III Player playing with his Bronze I friend for example. Either that, or you're playing in Ranked 5s or 3s.
To conclude: It's not your tier/division that determines who you play with, it's your hidden Matchmaking Rating (MMR).