Meaning of «intertemporal substitution effect dominates the income effect» Assume a household intertemporal optimisation problem, where they only either consume or labour, and one of the equilibrium conditions states that labour will be a positive function of productivity, when « the intertemporal substitution effect dominates the income effect».
The real wage is also a positive function of productivity, regardless of the above effects interaction.
How would one interpret the meaning of « the intertemporal substitution effect dominates the income effect», when there's a positive productivity shock?
My take on this is:

The intertemporal substitution effect refers to how easily the household substitutes consuming tomorrow for consuming today.
The income effect refers to how consumption by household will change, given a change in income. Income rises, and the household will want to consume more and work less.

Therefore, I would interpret the sentence «the intertemporal substitution effect dominates the income effect» as the household choses to work more today to consume more tomorrow, instead of consuming more today.
Am I correct?
I suppose the right approach is to start with the statement: &quot;Real wage is also a positive function of productivity&quot;.
Let's start with the income effect: If both goods, free time and consumption are normal goods (This is the standard case; normal good simply means: if you are richer you want to consume more of them), then the individual wants to increase both consumption and free time simply because he got richer and can afford it now. More free time translates into less working hours.
The substitution effect: As real wages increase the individual would miss one hour of higher salary after the wage increase. This makes free time relative to consumption more cost full than before. The substitution effect induces the individual to work more.
As long as the second (substituion) effect is greater than the first (income) effect labor demand will increase as productivity increases.

So far, the pretty standard interpretation for a change in relative prices. Regarding the intertemporal component of the substitution effect i found in Mankiw, Rotemberg and Summers 1982, p.8:

The intertemporal substitution hypothesis implies that labor supply should depend on the relative return from working in period t and from working in period t+1.This depends on the real wage in period t relative to the discounted real wage in period t+1.

I suggest this implies that as long as the productivity shock has a relative higher impact on real wages in $t$ than in $t+1$ the intertemporal substitution effect has a positive impact on labor supply in $t$. With all of this in mind you should be able to understand the proposition « labour will be a positive function of productivity, when  the intertemporal substitution effect dominates the income effect»