Interestingly, when McDavid his deal, his AAV was 16.67% of the cap at that time -- it was 15.72% of the cap for the year it kicked in.
If Matthews signs for $13.5 AAV this summer, that would be 16.16% of the expected $83.5M cap (assuming no agreement with the NHLPA to bump it further) and assuming a 23-24 of $88M, it would 15.34% of cap for the year it kicks in.
If he signs for $13M AAV, those numbers drop to 15.56% of the 22-23 cap and 14.77% of the 23-24 cap.
McKinnon's $12.6M AAV puts him at 15.27% of the 22-23 cap and 15.09% of the 23-24 cap.
A $12.8M AAV for Matthews would put him at 15.33% of the 22-23 cap and 14.54% of the 23-24 cap..
Incidentally Matthews current $11,640,250 AAV was 14.64% of the 18-19 cap and 14.28% of the 19-20 cap.
If you assume Matthews is around the same tier of player as MacKinnon, then a $12.8 AAV sounds reasonable to me.
It's arguable that the 23-24 cap number could be higher than $88M and that the 23-24 number could be higher than $83.5, which change both percentages for Matthews and the 23-24 percentage for MacKinnon. That could make a $13-$13.5M deal for Matthews more reasonable to me.
Incidentally, I use the two percentages (cap when signed and cap when kicked in) because while CapFriendly uses the first, the second is really more meaningful.