For NROTC, my son was advised that some units fill up more quickly than others. As students are offered scholarships, they will be assigned to the first unit on their list that has an open slot. So, your priority listing will be important.
Speak with the recruiter at the one or two colleges at which you are most interested and see how quickly their units fill up. Your top choice should be a school that you have been already accepted to or are reasonably sure you will.
When my son received his scholarship in December, he was assigned to the #1 school on his list, which he was reasonably sure he would get into. His "reach" school was #3 on his list. When he was accepted to that school in March, he asked for a transfer of his scholarship and was told that the unit was full and he would be waitlisted.
He kept in contact with the recruiter of the unit that he wanted to transfer to. The recruiter saw his sincere interest and persistence and worked to help him get his scholarship transferred once he knew who on his list was and wasn't accepted to that school. Once a slot was opened, the transfer was confirmed.
Keep in mind that each unit is different and the recruiter can be very helpful to a candidate who follows through. Commitment is a value that they want to see in a future officer.