Having a large number of small 110VAC mains transformers around, decided to try one out on 230VAC. Connected it up, and turned on the power. Took nearly 4 minutes for it to fail with a small pop and a flash as the wire blew out.
German made transformer, made around 1982. Got hot, but no smoke, no flames and only the pop as it went out.
It's all going going to depend on whether the iron core saturates magnetically or not. When the core saturates there's not much inductive resistance and a lot of amps can flow.
Dave's went up in seconds so I'm guessing the Weller cores saturate.
(and your core didn't)
Trust me it saturated, after a minute turned off the power and felt the core, and it was at around 50C, and after the winding shorted internally it was at that point you could smell it. Was hoping it would get to smoke point, but it failed before that. Taken a few apart before and there is no internal thermal fuse in them.
Should dig up that cheap voltage converter that has a fun function, it can work as step down or step up, and has a switch to select if the input is 110 or 220V, and another to select output of 110 or 220V, and of course it has only a fuse protection, and is rated at 100VA. Input is via the usual fixed cheap and nasty cable and output is via the (in)famous universal socket. At least that has PE continued through, unlike another that has a 2 wire mains lead, yet has an earthed socket outlet that connects to the case. That did have a first for me, the screws were tight, as in almost use impact driver tight, strange for a M4 screw.
As to transformers going internally short, very common, especially on those that have large capacitive loads on them, where the peak charging current of the capacitors heats up the wire internally, or for those run at full load with high mains input and then run at 175C plus till they cook.