Does facial fat transfer need to have structural support to be successful?

I've been told by a surgeon that fat grafting should be done after eyebrow lift and blepharoplasty to the lower lids as a separate visit after everything heals. He said fat needs to have structural support for successful grafting and should be done after all the tissue has time to heal. Is this true, will results be better? I've also had surgeon tell me they can do everything all at once without having to come in twice, needless to say less time to recover. Can someone please advise?