Well, it wouldn't make sense otherwise, would it? It can't be a tie since those are only between two adjacent noteheads (which need to have the same pitch and would not be used to connect two eighth notes when the first is on the beat: you'd just write a quarter), so one wants to hear four notes.
Which is what your fellows produced. Now the question is what the slur signifies: it can be a bowing instruction, or it can be a phrasing slur indicating a legato passage. A bowing instruction would typically also carry tenuto/portato bars. So it's likely a phrasing instruction.
The execution would likely not or barely tongue between second and third note, and try putting just as much tongue between the equal notes to make the attack just as distinct as the valve use between second and third notes would.