Oil rigs are compound entities. The storage tank you see is separate from the mining drill output buffer. There is an upper limit in the game engine on how much fluid can transfer each tick (default 6000) from the mining drill output buffer and the storage tank via the hidden pipe connection. When the mining drill is accelerated to produce more than that amount each tick, it can only run on alternate ticks.
I'm not going to change anything in Cargo Ships, but you can install this mod to increase the fluid transfer limit for all machines if you like: https://mods.factorio.com/mod/Fluidbox-Speed-Multiplier
