The first thing to say is that the laboratory personnel cannot diagnose a transfusion reaction. This may be a delayed haemolytic transfusion reaction, where the patient is clinically compromised, or it may be a delayed serological transfusion reaction, where the sample from the patient tests for a positive DAT and a "new" antibody specificity, that can be eluted from the red cells, but where the patient is not clinically compromised. This can only be diagnosed by the physician looking after the patient.
Secondly, the anti-Jka may be a de novo specificity, or may be present in the circulation as a result of an anamnestic reaction. Certainly, two weeks seems a bit quick for a de novo specificity to be detected, but it can happen (never say never in blood transfusion!), so it is more likely to be present as a result of an anamnestic reaction, although there must be a certain proportion of IgM immunoglobulin, as well as IgG.
As yan xia says, Kidd antibodies can cause complement fixation, but can only so do if there is some element of IgM present (anti-Jka that is pure IgG cannot fix complement), however, it is incredibly rare for Rh antibodies to fix complement (as far as I know, there are only two examples of anti-D described in the literature that have been able to fix complement - and just think how many millions of anti-D have been detected), so the complement on your patient's red cells is much more likely to be there as a result of the anti-Jka, than the anti-E.
Adding fresh serum does increase the sensitivity of the test (the so-called "two-stage IAT"), but treating the red cells with a protolytic enzyme, such as papain, and then performing the IAT is even more sensitive. An eluate can be used to "concentrate" the antibody sensitising the patient's red cells, but, be careful, as, is you are using a commercial elution kit, this may go counter to the kit instructions.