Yes, that is correct Matthews will be in quarantine now until he tests negative. That's how it works for everyone else, so that's how it should work for him.
This isn't going to be a "clean" playoffs if the players don't stay in the "bubble", or the "bubble" is pierced by someone else. If that's what people are looking for, then cancel the season. No revenue for the NHL, including the players who will receive a salary commensurate with 50% of the HRR revenue from last season.
I don't know exactly what the plan is for the NHL to have the playoffs, but it would seem to need the following elements:
1. All players enter the "bubble" now.
2. Starting now, every player and those in contact with them get tested frequently, if not every day.
3. After a period of time longer than two weeks when everyone in the "bubble" tests negative, then you start the playoffs.
This isn't going to work if the players and the staff don't maintain the "bubble".
Again, we may never have a vaccine, or it may be years away. The world can't afford to stop indefinitely for COVID-19. The NHL is not essential. If the NHL and NHLPA isn't smart enough to come up with a plan, and the discipline to execute it, then don't play and forego the revenue. The players should not expect to be paid for games they never played. The rest of the world will move on, return to some semblance of "normal" where our economy survives, and the NHL can wait for a vaccine.