I do this for a living as an facilities electrical engineer who works closely with electricians. The phase between lines on the primary side of a single-phase stepdown transformer is irrelevant to the secondary side. Indeed, sometimes the distribution lines are Y configuration rather than delta, so the inputs to the single-phase transformer is sometimes line-neutral instead of line-line. In most systems worldwide the single-phase transformer has two poles on the secondary side, one of which is grounded locally and is connected to the neutral conductor, the other pole is connected to the "hot" conductor or "line voltage". There is typically about 240V between hot on neutral. A main electrical panel for residential will have 2 bus bars in this case.
In the U.S., the transformer is typically has a three-pole secondary with a center-tap connected to the center of the secondary coil. The center tap is connected to local ground as well as the neutral conductor, and the other two poles at opposite ends are each hot conductors. Since there is only one coil on the transformer secondary this results in two hots that while measured against neutral are 120V, but each 180 degrees out of phase with the other for a result of 240V between lines. A main electrical panel will have 3 bus bars in this case. You can confirm this with a voltmeter. (If they were 120-degrees out of phase, you would measure a SQRT(3) ratio of V_lineline/V_lineneutral.
Occasionally in a commercial or industrial facility, you may find a 2-pole electrical panel that is a sub-circuit to a three-phase Y-configured panel (120/208V Typical configuration). These tend to be remodel conversions from when the building mains were swapped from single-phase to three-phase. In this one case, you will get the 120-degree difference between lines. When this is the case you have to be extra careful when connecting loads to the subpanel, because the difference in line-line voltage is less than what you would expect at first glance, and some equipment may fail to operate, or operate in a degraded state, because of that.