I have gone through the attached file. Please clear some of my doubts

1) how did you measure different constructs (multi item or single item)

2) if these were multi item constructs how you generate the interaction variable (product indicator approach or ????).

3) As per your hypothesis you must run multi-group analysis (high and low social support)

I have attached my papers where you can have an insight into the procedure

Article Factors affecting Cultural Intelligence and its Impact on Jo...

Article Cultural intelligence and job performance An empirical inves...

Ahmad, your interpretation is correct, unfortunately.

If you used the ML estimator for estimating the parameters of the product-indicator approach, the standard error of the product term may be biased (too small), i.e. not correctly estimated. Then, your moderator effect would be an artifact.

We did a simulation study where we compared two product indicator approaches with two distribution-analytic approaches, LMS and QML. The results show that the SE of the moderator effect was generally underestimated:

Moosbrugger, H., Schermelleh-Engel, K., Kelava, A., & Klein, A. G. (2009). Testing multiple nonlinear effects in structural equation modeling: A comparison of alternative estimation approaches. In T. Teo & M. S. Khine (Eds.), Structural equation modeling in educational research: Concepts and applications (pp. 103-136). Rotterdam, NL: Sense Publishers.

It would also be necessary to check the assumptions of the estimator: Are the predictor variables normally distributed? If not, this could also be a reason for your finding.

Regards, Karin