If you look at the precedence list in perlop, += is of higher precedence than ,, so it will be run first, just like the multiplication will be run before the addition in $c+$c*$_
In $c+0, $c+=1; + is the highest precedence operation, so addition is indeed run first. In $tmp = $c, $c+=1; = and += are of equivalent precedences, and so are run from left to right (and that's because of the , in between).
Edit: added a ; here and a ; there, because their absence made my post look confusing.
Edit: ikegami is right, I mistook precedence for evaluation order, and just kept being blinded by that mistake. Please read his explanation, which involves more perlguts, but isn't misleading.