Hi Oldan,
Not sure where the issue is? I don't see it to be honest, as you mentioned already:
Their website states that "This case has integrated Erica Synths PSU capable of 1.25A per rail (2.5A total)."
And then you checked your PSU (good by the way to check!) and you found this:
OUT ±12VDC / 1250mA (thus -12 V at 1250 mA = 1.25 A and +12 V at 1250 mA = 1.25 A, together 2.5 A; I assume, unless the manual of that PSU says differently)
So that's the same, isn't it, so... where do you see an issue? Did you bought this Erica Synths case new from Erica Synths or an authorised Erica Synths dealer? If yes, then this should be fine.
You could start with one module, then two, etcetera, in case you are still not sure but I don't see an issue.
Have fun with modular and kind regards, Garfield.
For review reports of Eurorack modules, please refer to https://garfieldmodular.net/ for PDF formatted downloads