I'm a public school K teacher. We use RESULTS for Language Arts assessment in my district, and the benchmark math tests that come with the particular curriculum we use - each basically tests math content up to that point in the year. They're administered quarterly, right before I do report cards.
The RESULTS are done orally 1:1. I usually do the Math Benchmarks in small groups (3-4 kids with me) except for the first quarter, which is also 1:1. Of course, I read the directions to them for it. Oh, we do a writing benchmark test too - that we do whole group though I meet with kids 1:1 if I can't decipher their work by myself
The RESULTS in particular is very valuable info for the first grade teacher and does seem (to me) to correlate very strongly with reading level in first grade and beyond. We use the info to mix the classes up for next year, for the next year's teacher to plan curriculum that addresses her students' needs, etc. Also, throughout the year I'm always using my assessment results to plan small groups for kids who need help with particular skills. The most interesting use in my opinion is to track progress throughout the year.
I would guess they're just going to give the same assessment they give to the public school end-of-the-year K's. I actually did one today on a preschool student who might move straight into first grade.
The kindergarten grade has standards that must be met just like any other grade. So it follows that assessments that measure those standards (we hope) are given.