At what point do I add my reactivated starter to my dough recipe?

I've taken my starter out of the fridge and done a 3-cycle refresh (1:1:1...wait for it to double and fall back; throw half out and repeat).

I now want to use it in a recipe.

At what point do I add the starter to a recipe?

Immediately after I refresh it?

An hour after I refresh it?

Just after it rises and falls back after I refresh it (6-12 hours later)?

It seems to me that using the starter after it has risen and fallen back means the yeastie beasties have exhausted whatever food there was and I'd be adding that useless food to the new dough, albeit with a maximum yeast population.

Thank you for your help.