What I do when wiring a mains transformer, is to solder the connections as per the datasheet & before applying mains power, I hook up my signal generator to the mains transformer.
If you put 1v (at about 60Hz) onto the primary, set your voltmeter to AC volts & measure across the primary. There should be no drop across the primary windings. If the level drops acroos the primaries, they are out of phase, swap one of the windings.
Measure the voltage on the secondaries. Each secondary should read about 130-140mV . Across both secodaries should give you double, about 270mV or so.
Once I am happy with this, I connect the transformer to the mains. I have made up a mains cable with a fuse holder & 100mA fuse inline, so if there are any shorts in my transformer, the fuse will blow rather than the transformer or the house circuit breaker.
Do not connect anything to the transformer secondaries yet.
I switch on for a few seconds, & switch off. Smell for anything odd, smoke for e.g. Check the fuse. If everything is OK, switch on again, measure the voltages on the transformer secondaries, should be a little more than 15v, around 16v with no load (PSU) connected. Be aware of any excessive heat anywhere, hot resistors or diodes, etc.
All OK? Now connect the PSU circuit to the secondaries. Switch on, switch off, smell again. Once happy, switch on again & measure to check the voltages on the outputs of the PSU.
Then connect the project to the PSU, & go through the same process again. Checking the rail voltages is the first thing to do. If your +15v or -15v (one or the other, or both) are not reading correctly, there is a problem.
Just call me Mr Cautious Wink