Dear Luis
Along with the differences organization determination profile , check the partner function on which the org determination is dependent for these transactions.
In case of interaction record it may be possible that you have given a value for the field : Partner function ORG in the customizing as contact person , since it is giving a message for selecting contact person and preventing the org selection to appear.
Hence you will first have to chose a contact person or enter a contact person on the interaction record to trigger the Org determination.
/Hasan