Close, but let me draw a better picture in your mind. You must first remember space is a medium, we don't know of exactly what, but know it's at 2.7degrees.
Imagine it as the sea, and you, swimming, can only do 3mph.
A ship comes past at 3mph, but it's hull is one vast pool of water. The guy in it is swimming at 3mph, but doing 6mph with respect to (wrt) someone watching through a telescope from the land. Floating in this pool is a smaller boat hull, also filled with water, being towed towards the front of the ship at 3mph. A guy dives in it and swims at 3mph. The guy on land sees him doing 9mph! And so on and so on.
Each hull and each swimmer create a 'bow shock' wave as they move through the water. In the medium of space that's what propagates the excitable particle activity we see (synchrotron radiation and 'photoelectrons'). The particles are concentrated at the front of the field, at the boundaries between 'lumps' of field, they are NOT the field itself.
Similarly, if there's a water jet blasting into the pool from under you, and you dive into that, you'll do 3mph wrt the water in the jet.
If you search the web you'll find a movie of the gas jets of Messier 87. The mass being sucked in isn't constant, so neither is the stream coming out, it's a bit 'blobby', but the blobs are moving at 6c viewed from our telescope. (which could also be on a 'ship' moving the other way!).
In other words; If you're a swimmer jumping in a pool you don't care a jot what speed and direction the ship you're on is moving, and you don't have to do 3mp wrt someone watching from another ship doing 20kts the other way! You always do 3mph LOCALLY through the water you're moving through.
In M87 there are probably ionised particles being ejected with their own local field 'medium' around them, these ejected lumps of space could do 'c' wrt the medium that went before, the stream spreading out with distance. The fastest speeds will therefore be seen close to the black hole, as everything will gradually slow down.
I hope you can now visualise the very simple and familiar physical process? - combining Locality with Reality.