In Pandemic, when does the discard-over-7-cards rule take effect?

Scenario

Pandemic's excess card rule states that if you have more than 7 cards in your hand at any time, you must discard the excess (according to your preference, of course).

Let's say you're the Scientist, have 5 city cards and 2 special cards (like the airlift, or research center build card). The Researcher comes to town and gives you the remaining 1 color city card that will allow you to cure a disease as soon as you get to a research facility.

Let's also say there's only two players (Researcher and Scientist). And that this is the last color that needs to be cured.

This takes you to 8 cards - over the amount allowed.

Question

When do I, as the Scientist, need to play / discard my excess cards (in this case, let's take the two special cards as the ones to play) so I am not in violation of the excess card rule, but also so I maximize the value of the Researcher's endowment of city cards?

edited to reflect the limit of 7 vs 8, as noted by Gendolkari

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First, note that the hand limit is 7 cards, NOT 8 cards!

You cannot hold more than 7 cards in your hand for any length of time. This means that while you are holding 7 cards, the researcher cannot give you 2 cards. Actions are one at a time, so first the researcher would give you a card, at which point you would be over the limit. Before any other action is taken, you must discard down to the hand limit. Once you are at 7 again, the researcher can give you another card now, at which point you will need to discard again.