Well, asking for "tips for playing Latin rhythms" actually asks for a dissertation. But here are some things to bear in mind for that one particular chart, which I'm listening to right now.
1) This is a samba (although the recorded tempo of 132 or so is really too fast to actually dance to). A samba is in TWO, not four. I don't know whether the chart is written in 4/4, 2/4, cut time, or what, but it's in TWO. The characteristic rhythm of the samba (and your feet do this when you dance the samba) is dotted quarter, eighth, dotted quarter, eighth, on and on. If it's notated in four, the heavy beats (where your foot hits the floor when dancing) would be ONE and THREE (but as I note, the entire feel of this form is in TWO). So if it's notated in 4/4, those quarter notes are actually functioning as eighths - two notes per felt beat, and the eighths are functioning as sixteenths - four notes per felt beat.
2) No swing feel. The dotted-quarter-eighth of the samba is the feel, not swung eighths.
3) Your articulation HAS to be precise. Most of the tutti notes will be tongue-clipped at their ends. Not so short as staccato, but separated. TAAAHT not TAAAH DAAAH or T-T. Even listen to the soloists and they play that way too, far more precise heavy articulation than if it were a swing tune.
I'll be honest, you might well get a better handle on this by cueing up some "Dance the Samba!" instructional material and learning the steps, than anything else.
On the other hand, if no one else especially in the rhythm section understands what a samba is and how to play it (which derives from how you dance it), you may just be forced to go along with the majority.
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