How Long to Wait Between Surgical Cosmetic Procedures?

there does not appear to be a contraindication to having both procedures done 4 days apart. If, however, you do not feel well during your few days of convalescence, give your body a chance to heal more and delay the fat injections.

Liposuction has been used for breast reduction but is only of use if the excess breast tissue is composed mostly-entirely of fat (which is not always the case) and the skin is sufficiently elastic to shrink after liposuction. This skin only exists in younger patients who incidentally have more breast gland tissue than breast fat tissue. It should really as the sole means of breast reduction for smaller reductions that health insurance commonly does not cover. In fact many health insurance policies specifically state that they do not cover breast reduction by liposuction alone.
Immediately would mean right afterwards but it appears you plan on having the fat grafting 4 days later. The question is: Will the second surgeon use the first surgeon's harvested fat or will he/she get it from elsewhere on the body? The survival rate of the fat will be significantly less if you put it in the refrigerator and inject if 4 days later although some surgeons have reported doing so and getting good results. I personally do not see the need for that as you can just liposuction the fat from one area and minutes later inject it into another area of the body for the best survival rate.
There is something amiss about a plastic surgeon specializing in the buttock and another in the breast. Any plastic surgeon who is experienced with free fat grafting is obviously experienced with taking that fat out by liposuction from other areas of the body. If you saw a few plastic surgeons in consultation and only one was willing to do this liposuction breast reduction I would probably not have that surgeon do the procedure if I were you. There are increasing numbers of doctors out there who say they specialize in one procedure like liposuction and do nothing else other than that procedure whatever it is. On closer inspection you will find that their training is lacking or they are not plastic surgeons. That may or may not be the case here as you posted question is short on details.