That is indeed how it is supposed to work. But things haven't exactly been working like they're supposed to lately.

For FY26, when we had a PBR proposing massive cuts followed by a government shutdown with a long stretch where NASA didn't know what their real budget was going to be, we saw a bunch of layoffs and project cancellations in preparation for a budget that might resemble what the president was requesting. Whether or not that was legal is in question:

https://democrats-science.house.gov/imo/media/doc/SST%20Mino...