The reason why tamoxifen-inducible systems exist is to study your gene of interest at different stages of the mouse's life. Technically your only limitation is the level of expression of your Cre recombinase. This means that in your case the adipocyte-specific promoter should drive the expression of the Cre-ERT at the time of injection with tamoxifen. The timing of your injection is therefore dependent on the scientific question you are trying to answer. The age of injection will, therefore, depend on what you want to investigate (there is no standard age for tamoxifen injection).
Some say that younger mice are more sensitive to tamoxifen and mice are typically used at 6–8 weeks of age for Cre induction by tamoxifen. Of course, genetic make-up and the type of Cre-ER transgene used also make a difference in the sensitivity to tamoxifen treatment at different ages. Good luck!