I can understand that the alchemy system currently in place is a bit confusing when you never got it explained to you so i will try to explain it as easy as possible for everone to understand.
The level on the potions isn’t reflecting the level of the mage doing them at all but rather the level the potions are. Some potions can go up to level 5 while other have their max at level 2 or zero levels even. If a potion have a max level of 2 for example, it will be harder to reach the second level of that kind of potion then reaching level 2 on another potion that have a max level of 5.
To increase the potions level can be done with either higher alchemy or being higher spec mage or both, but you can never go above max level of that kind of potion.