My son's sport is not swimming, and I don't even know what a junior national cut is, but I appreciate all the advice I've received so far, so I'll add a little to the conversation.
While time-based (or individual rank-based) sports might not require as much of a look by the coach as other sports, you and your student should still want to see the coach because your student will be spending so much time with him or her over the next four years!
My son is looking at DIII colleges. We have found that a lot of advice will be given that applies to DI but not DIII. For example, the July 1-after-junior-year contact date for coaches applies to DI but not DIII. In fact, DIII coaches can go ahead and contact students now. Students can contact coaches whenever they'd like to do so in either DI or DIII. You might want to read the NCAA rules (on the web) so you'll be well-informed about the rules.
We organized his top colleges into groups for visits over his upcoming spring break, and contacted those specific coaches to see whether they would be available for us to meet them. I agree with the poster who suggested filling out the online recruiting forms and emailing coaches now.