They will not need antimatter for their own abilities (only refueling) but will rapid generate it in an AoE based on the tanker level and when in a plasma storm or within refuel range of a gas giant. They are capital ships.
Their own antimatter regeneration rate is zero--they can only tank up at a suitable system or a star (I forgot stars) and they will have a large capacity for storage.
The fact that they are prone to blow up and cause area damage makes them risky to have in combat near a fleet. The refuel range will also be their death damage range.
The ships above are modifications of the unused vanilla Sins refinery ship for the Advent, an enlarged and "winged" Vasari refinery ship and one of the robotic ship meshes attached to part of a phase inhibitor for the TEC.
The concept is these ships are ramscoops that siphon hydrogen, helium and methane from planets and stars by dipping into their atmospheres.