It appears as though that piece has been recently typeset (along with quite a lot of Cima's other work) by a contributor to IMSLP. It is not a professional publication, but I believe it is meant to be as accurate to the composer's original work as possible (hence the listing of "Urtext" at the bottom of each page.)
The rhythm and meter would be odd in present-day context, but while I am not an expert on renaissance notational style, there are various things being done in the typesetting that appear to be consistent, and don't seem out of place in renaissance-era music. For example, see the full score posted with this same typesetting. The cornetto part is completely consistent with the score, and the quality of typesetting appears quite good. You will also note the use of breve rests and the longa (i.e. quadruple whole note) placed at the very end of the piece. We don't see these symbols at all in present-day music, but I believe they are being used correctly here.
If I recall correctly from the very minimal amount of renaissance music theory I did learn in college a number of years ago, the actual metering does not have to be consistent with the time signature. Throughout this piece, the meter changes from 4 to 8 to 16 without a "time signature change" as we know it, and that's okay. The "c" - common time mark listed at the top of the piece is not meant to denote 4/4 time, but a type of tempo or pacing.
Another point I'll make in favor of the quality of this typesetting is to use another of this composer's works uploaded to IMSLP that is in a professionally published format as an example: http://javanese.imslp.info/files/imglnks/usimg/5/56/IMSLP28238-PMLP62029-Cima_Ricercare_Organo.pdf
Many of those "oddities" are here as well, and used consistently. The "time signature" is not used to denote meter, we see usage of breve rests and 8-beat measures, and later breve notes.
And lastly, the typesetter/editor himself does appear to have some legit credentials.