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The pump creates a 'Supply' signal...it has (whatever is connected to any of its inputs), does anything it's connected to its output(s) want what it has.
Tank #3 replies with 'yes, I can take oil, give me oil', so the pump goes wild filling it up.
Tank #2 replies with 'I'm connected to #3, I can take oil, give me some too', and will get oil at a slower rate.
Tank #1 isn't connected to Tank #3, so it's "deaf" to the signals; it can't communicate with the pump and gets nothing.
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To set up an effective 'buffer' system, you need to put pumps (transfer stations, conveyor engines, etc) between storage buildings, which will keep the material as close to the consuming building as possible. If you want 2700 tons' worth of storage for that refinery, your best bet is [Existing Pump] -> [1-in-3-out pump on output of existing pump] -> [one tank on each output of 1-in-3-out pump] -> [3-in-1-out pump connected to the outputs on the 3 tanks] -> [refinery connected to the output of the second 3-in-1-out pump]. That'll give you the ability to buffer 3150 tons of oil...2700 for the tanks, plus the 450 for the Refinery's internal capacity [as that last pump will try to keep the refinery topped up].
Keeping buildings topped up isn't as critical for a refinery, but for a Power Plant that shares its supply with other stuff [such as bricks factory] having that last pump in place buys you time to fix any supply disruptions...the power plant can hum away on its internal stores (100 tons) instead of shutting everything down the instant the supply gets disrupted.
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One last hint: I chose my words carefully earlier when I said 'whatever is connected to its inputs'. "Pump" buildings can work with multiple types of resource, they don't have to be dedicated to a single resource the way storage tanks / aggregate storage are.
You can, for example, go refinery -> pumping station -> rail loading/unloading, and it'll work for both Bitumen and Fuel. Or go "separate coal storage + iron storage" -> Conveyor Engine -> Steel Mill, and it'll keep the factory supplied. It might become a bottleneck late game [as a single pump can only handle something like 10-12 tons per second], but does work.
Factories and storages are passive. If one is full it overspills to the next receiver. But that is slow.