What I suspect happened –
Tank refill = more weight/pressure
Leaking from the back valve of the stove = too much pressure on it; “reservoir” (the weakest point) overflows, especially if downstairs heater kicked on/off (draw oil, then stop = pressure up line)
I’m not good with fluid dynamics lol but I think, in theory:
Since the tank valve was shut last night, any oil in the lines probably was used up by the downstairs heater – lines are dry. (You can test this by opening both valves on the stove – does oil flow in? Will also empty the reservoir tank that is leaking on the back into the stove bottom/create headspace for more oil)
That means in theory, if you open the tank valve, it’ll refill the empty lines without creating excess pressure.
Someday we’ll replace the junction with a Y split, not a T split, which should help some of these weird issues that come up when the tank is either too empty or too full…but that requires copper pipe and welding.