Right, you need actual placement, not just sending them. And you definitely do want to remove the penalty all at once, ideally in the same month in which you remove your isolation penalty.
I started a recent game w/ Chimu, where I got some real luck. In about 1510, the Spanish TPed Cartagena. So I met them, and instantly sent a state gift. Relations in the 80s, IIRC. They were their alliance leader, so I joined them. Then, luck: not too much later, they DoWed France. So I got invited, and DoWed as well. Next month, I have diplomatic relations with France: I can see Ile de France, including CoT! So I quickly made peace w/ France, and sent them a state gift. So, boom, +200 relations.
Meanwhile, I've examined my tech. Through the 1400s, I've invested equally in all four techs, which are all more or less out of reach (cost 30000 or so for infra 2). By this time I've got about 15000 in each tech, more or less. So I watch the CoT in Ile de France... there's an empty slot. I send to it. Success! OK, one whiteman down; tech cost dropped about 5000. So I know I can get two more whitemen off without hitting the tech level. So I watch... two more empty slots later, my whiteman is up to 3, and my tech bars are almost complete. I wait for one more empty slot... it takes about 8 months.
The one thing that's tricky here is that merchants take a month to arrive. So, in the month I see the slot empty, I send all 5 merchants that I have. (I would have sent 6 if I had had all 6.) Then the next month, I wait to see how they did. So long as even one succeeds, then my tech is going to go up, and I want to make that count. If none succeed, though, then I don't want to swap maps so as to try again at the next empty slot. Ideally, two would succeed. In my case, two did (the first got the empty slot, and one of the others bumped a European). As soon as I saw the result, I swapped maps with the French, negating the isolation penalty at the same time as whiteman, which meant I did not waste any of my tech investment.