Sometimes it is an accurate prediction and sometimes it is not. The system simply looks at the amount of DNA in common and then calculates it based on that. It does not attempt to determine the "removed" level. You must figure that for yourself with the paper tree. 1st to second could include a 1st once removed or even a 2nd once removed.

Also keep in mind that DNA recombination is random. You and the other person may get different amounts at different locations than each other so this can throw the calculation off.

My aunt shows as a 2nd to 3rd cousin to a particular relative. This is very good as she is a 2nd cousin once removed. This same person is my 3rd cousin but we didn't get that amount of shared DNA from our common ancestor and this same person shows as a 5th to 8th cousin in the DNA calculation for me despite being a documented 3rd cousin.