transformer - Toroids low magnetic field is only for the core?

Here is a thing. When I connect it as 120v (parallel), the magnetic field outside the core is much lesser than when connected as 240v (series). The load of both is same 100v-256v autovolt LG OLED TV (just for testing).

Does it mean when connecting as 240v series, the windings don't have uniform current? Why? How?

It's for this model http://catalog.triadmagnetics.com/Asset/VPM240-2080.pdf, a 500va medical isolation transformer I bought to protect my bench project troubleshooting.