Positive interaction term with one negative component?
Ignore the other variables. Let $g$ be growth, $C$ corruption and $A$ aid. You look at

$$g = \alpha C + \beta A + \gamma A\cdot C$$

You ask, "does lower corruption increases the effectiveness of foreign aid?"

For this you have indeed to examine the cross-partial derivative

$$\frac {\partial g}{\partial A\partial C} = \gamma$$

This is "how growth is affected at the margin by Aid, if corruption changes"... So if lower corruption increases the effectiveness of Aid, $\gamma$ should be negative, not positive...

...if your corruption index is mapped as "the higher the value of $C$ the higher the corruption".

If your "corruption index" is mapped in reverse (and so in reality it measures "non-corruption"), the anticipated sign reverses also.