perhaps a stuck close thermostat? just shooting ideas on what else might be worth checking ...
it's weird the coolant boils same way on 2 new rads ... if coolant boils then loss in level is normal as some of it will be either spit out through the vent on return tank or it will evaporate (steam away) fast.
good thing there is no leaks in system on the new rad. I honestly doubt you have a bad head gasket ... yet. I wouldn't run it too much until coolant properly circulates and doesn't boil anymore.
JohnGD suggested a good test to check if exhaust gasses are present in coolant (looks like air bubbles).
is it a V6 or 4 cylinder? they have opposite direction of coolant flow between the two.
water inlet pipe on 4 cylinder is located at radiator top (thermostat under alternator) while V6 1mz-fe has the water inlet pipe (hose at radiator bottom) on the driver (LH) side of engine, buried under bunch of other stuff.
when was the last time someone checked/replaced the thermostat with its gasket? it's only $18 for new OEM parts (online dealer), but a few hours of labor on top of that (at least for V6).
other cheap thing as mentioned, get a new radiator cap from dealer (go OEM on this one please), it's only a few bucks and takes 5 seconds to replace (do it on cold car). it's a cap sitting on top of rad (4 cylinder model). your aftermarket rad probably has an aftermarket rad cap.
V6 models have rad cap actually on engine, not on rad itself
and the last thing which comes to my mind ... did someone check that water pump actually spins and has the fins intact (and not e.g. corroded)? when was the timing belt and water pump replaced for the last time?