The reply from ERich sums it up well. The explanation of swapping the primary leads of one transformer will be easier than jumpering the heavy gauge secondary leads.
The main factor of knowing when the secondaries are phased properly for this application, is because the secondary conductors will be heavy gauge conductors, and this could pose a physical parts layout problem (particularly if you've already chosen an enclosure for your project). The phasing factor is a result of the direction that the windings are wound around the core. Since it's undetermined (because the primaries were existing windings and usually covered), although it's not really important since you're working with two xfmr cores and you'll be adding your own secondaries.
The phase can be checked by winding a few turns of any small conductor on the cores. Two secondary leads from separate xfmrs are connected and two are left separated. When the test confirms that you've got the leads connected correctly, you'll want to wind your secondaries in the same direction as the test windings, and you'll want the four primary windings to retain the same relationship to being paired together.
If you dont have your secondary windings wound yet.. A low voltage test light will light (6 to 12V) when connected across the open leads when the windings are not correctly connected or out-of-phase for the application you want. This is the unwanted maximum current condition that ERich mentioned. This lamp test will show how the the xfmrs are phased. You would probably want your secondary windings to be wound for your convenience, in that the leads can be attached in parallel to the soldering unit's output cables or terminals, without any leads needing to be much longer than the other set.
You can bond the xfmr frames to the unit's safety earth ground in the event of a component failure.
WB ................