They needed to stay below about 6000-7000 US deliveries in June. It's hard to know for sure because we don't know how many Roadsters were sold in the US after the program started. The program's start date is shortly before they switched to selling Roadsters oversees only (the last year of production was 100% export because there was some safety feature they would have had to add to sell in the US).
6000 a month is a very new thing for Tesla. As recently as February of this year they delivered less than 6000 cars in the US. In April they were just a bit above 6000. May was the first month in the company's history that was way over 6000 deliveries (about 9000). There is evidence they have been slow walking some deliveries. Also they chose June to start shipping Model 3s to all the stores in the US. A number of stores are giving test drives for Model 3s now. If they also shipped some cars for service loaners, that would absorb some more production.
Car registration numbers for other countries indicates that a lot of Ss and Xs were delivered overseas in the last month.
In May Tesla was prioritizing Model 3 deliveries to Washington State so as many people as possible could take advantage of a state tax incentive that expired May 31. According to a number of Washington reservation holders who just missed the end of May deadline, their delivery estimates almost all went to July. That's another indication Tesla was planning on delivering fewer cars in the US in June after pushing them to Washington in May.
There is no guarantee Tesla did manage to push the 200,000th delivery to this week or next week, but if they missed and delivered last month, that's a screw up on their part. The evidence Tesla was trying to slow walk US deliveries to stay under the threshold is strong.