It looks like this is another border change we have Nikita Khrushchev to thank for.
The commission that decided the administrative border between the
Ukrainian SSR and Moldavian SSR inside the Soviet Union was chaired by
Nikita Khrushchev, the then leader of the Ukrainian SSR and the future
USSR leader who would add Crimea to the Ukrainian SSR.
As for the rationale, what I was able to dig up was the following:
On 2 August 1940, the Supreme Soviet unanimously approved to dissolve
the old Moldavian ASSR ... Northern and southern
parts of the territories occupied by the Soviet Union in June 1940
(the current Chernivtsi Oblast and Budjak), which were more
heterogeneous ethnically, were transferred to the Ukrainian SSR,
although their population also included 337,000 Moldovans. As such,
the strategically important Black Sea coast and Danube frontage were
given to the Ukrainian SSR, considered more reliable* than the
Moldavian SSR, which could have been claimed by Romania.
The reference given for this last statement was: King, C. (2000). The Moldovans: Romania, Russia, and the politics of culture. Stanford: Hoover Institution Press. ISBN 9780817997915. It would probably be worth tracking that down as a more direct source, to see more precisely what was said about it (and to track down his sources).
But with what I have available right now, it looks like the claim is that the main reasons given were matters of geopolitics. Henry in the comments above helpfully posted a census map of the area from the next year (1941). I've circled in red the areas that were given to Ukraine SSR.
It shows that all the counties in the new Moldovan SSR were majority Romanian (although 2 with much larger minority % than any nearby counties), while all the ones given to Ukraine were not. Of Budjak's 3 counties, 2 were majority Russian or Ukrainian, while the 3rd was only about a quarter Romanian, and very nearly a majority Bulgarian. So the claimed concern that Nationalist Romanians would be far more interested in taking back those other Moldovan SSR counties, and locals there more interested in reuniting with Romania, probably holds water.
The Budjak was also the bit encompassing the Black Sea coast, which contained the USSR's only real year-round ice-free ports. That was a big deal for the USSR, and not an area they'd want to court any more instability than necessary.
I think those reasons are both what was claimed, and sufficient, so we've got no good reason to be unsatisfied with them. However, a cynic might point out here that Khrushchev happened to be the party official in charge of Ukraine at this time, and making his own little internal political empire stronger in the (literally) cutthroat world of USSR party politics probably had its attractions too.
* - "Reliable" in this kind of context usally means "loyal to the central government." or "Less likely to ignore orders or rebel."