Sign of substitution and income effect of a price change

You are correct on the main point. The effect is the derivative of the demand with respect to its argument (price or income), the sign of which does not depend on what the size or sign of the change in the argument is.

You did make a mistake: the income effect is positive for normal goods, negative for inferior goods.

The income effect is negative for normal goods and positive for inferior goods. That is, you buy more normal goods when you are richer and less inferior goods.

In contrast, the substitution effect is negative when price increases and vice-versa. It always moves opposite to the price sign.

Understand the difference between the effect of income change and income effect. The effect of change in income on the demand of good under consideration is positive but in microeconomics theory income effect is something different. The effect of change in price of good is decomposed into income effect and substitution effect. These two effects occurs when own price changes rather than the change in the subject of substituted good or change in income. Income effect means when price of a good increases(decreases), real income of consumer decreases (increases), so quantity demanded of that good decreases(increases). Therefore, decrease (increase) in real income causes negative relationship between quantity demanded and price. The negative relationship between quantity demanded and price is shown through income effect of the price change. So we call income effect is negative for normal good. Actually income effect shows the negative relationship between quantity demanded and price. Substitution effect means when the price of a good increases (decreases), it becomes more expensive(less expensive) thn the other good, therefore its quantity demanded will decrease(increase). Substitution effect also shows negative relation between quantity demanded and price, so substitution effect is also negative. Income effect is positive in case of inferior good and substitution effect will be negative in both cases.