I suppose another way to look at this is on a grid. It might not serve as an effective aid, so feel free to ignore this.
Before Alchemy, cost was on a one-dimensional number line. You could map cost from 0 to 8. An increase or decrease in cost was pretty easy to map out.
Now comes Alchemy. Look, a new cost. We no longer can measure cost on a number line. Now we get to use a Cartesian plane (the x-y coordinates you learned in algebra). On the x-axis, you have the cost in coins. On the y-axis, you have the cost in potions. The costs of most cards will still be a line where the coin cost is 0-8 (and soon 11) while the potion cost is 0-1. No card requires multiple potions, but there could be in theory. You can draw a rectangle to illustrate the cost of potion cards.
Cards like Bishop and Salvager only care about the cost on the x-axis. The y-axis does not matter. Apprentice specifically looks at the cost on the x-axis and then assigns a number based on the cost on the y-axis. If you're familiar with complex numbers, it'd be like saying that you get $2 for each multiple of i. If you're not, then you probably shouldn't be reading my unnecessarily complicated analysis anyway.
Cards like Remodel and Expand give you a wide range. You can Remodel into something that costs up to 2 more. So, take the cost on the x-axis and add 2 to it. It doesn't change the y-axis at all. You now have a slightly larger rectangle. You can gain a card which cost lies in that rectangle. If Potion=1 then the new cost can also include Potion=1. Saboteur does the same thing. Shrink the rectangle down by 2 and look for a cost that falls in that rectangle. If that rectangle is actually a line, then you cannot take something that costs a Potion.
Cards like Upgrade and Remake are more specific. They say exactly 1. The understood rule is that the number refers to the number of coins. So, you go up or down on the x-axis, but the y-axis does not change. If the card has no Potion cost, then you have a line illustrating the cost. Add 1 to the right of the cost and mark it with a red dot. The new cost must be that dot. If the card has a Potion cost, you do the same thing. The problem is that you don't change the y-axis at all. So, the red dot is one higher on the x-axis, but the Potion cost does not change. If there were a card that says, "Gain a card costing exactly 1 more Potion," then you could go up on the y-axis.
I would love to add actual illustrations to this, but I don't really have to time to fidget with that. Sorry. Not really sure that my explanation is really any better. It's just a different way of approaching it.