Is aluminium amphoteric?
Yes, you are right. The reaction depends on with which ion it is accompanied with. Note that these species are in equilibrium and present in the solution  and that particular reaction proceeds according to which ion is present in the solution in concentrated form. 


Aluminum hydroxide is formed when soluble salt of $\ce{Al^3+}$ i.e
$\ce{[Al(H2O)6]^3+}$ when it is reacted with base. 

$$\ce{[Al(H2O)6]^3+(aq) + 3 OH-(aq) → Al(H2O)3(OH)3(s) + 3 H2O(l)}$$

This insoluble metal hydroxide can act as a base, since it can be
redissolved by reacting it with an acid.
As Brønsted base

$$\ce{Al(H2O)3(OH)3(s) + 3 H3O+(aq) → [Al(H2O)6]^3+(aq) + 3 H2O(l)}$$

Alternatively, the metal hydroxide can act as an acid, since it can
react with a base.
Lewis acid

$$\ce{Al(H2O)3(OH)3(s) + OH-(aq) → [Al(H2O)2(OH)4]-(aq) + H2O(l)}$$


Thus, all aluminium compounds are said to be amphoteric.