Well the Jays are going to make their decision based on more factors other than just what Matz is worth. They'll be having conversations with his agent to try and find out what Matz is leaning towards doing. If they get the feeling that he is really leaning towards testing the free agent market because he and his agent feel like his value is at it's greatest right now, then it's a pretty easy decision to start with the 1 qualifying offer to ensure that if he doesn't sign here, the Jays will get a compensatory draft pick back. That comp pick has a pretty good chunk of value attached to it on it's own.
Second, offering the QO doesn't eliminate the chances of also offering a multiyear deal later if his market isn't what he thought it was. But at that point, maybe Matz and his agent feel like 1 year at 18.4, would be better than 2 at 23 or 2 at 24 + an option. It that happens, sure, it's an AAV overpay, but it's only a 1 year deal with almost 0 downside. Signing him at 1 year 18.4 vs 2 at 24 is a 6 million difference in AAV but only for 1 year, so its not like that 6 million is going to hamstring them for years to come.
The QO is just the Jays safety net to get the comp pick if he goes elsewhere. That pick isn't just about getting a pick either, it makes the Jays signing bonus pool go up which gives more flexibility to go over slot on guys they want to go over slot on without penalty. There's lots of potential value in getting additional comp picks when you can get them aside from just getting another minor league player.