When do incisions typically close after just a BBL procedure? I was told 1 week. Is that true?

It is just a matter of semantics: we “close” them at the end of the procedure. The wound healing process takes days, weeks and months, or even more. The wound is basically sealed after 48 hours, strong enough to have the stitches removed in 7 days, and practically “healed “ in three weeks. The rest of the time is for the process of maturity.
Best Regards

Incisions should close within a couple days but leakage of some fluid for longer may be totally normal. If you are concerned, your surgeon would be happy to evaluate you virtually or even in person to put your fears at ease. If you are leaking pus or foul smelling material, that would be a sign of infection that should be treated promptly.

There are benefits to either method (closing, leaving open), and I would recommend that you decide the surgeon based upon experience and results. No drainage after liposuction is unusual, but the amount of drainage can vary quite a bit depending upon the number of areas liposuctioned, the volume infiltrated, the amount of lipoaspirate, and the use of sutures for closure of liposuction ports. The fluid, if not present as a collection, should be absorbed. I personally do not use drains for liposuction, but every surgeon has different protocols. I make very few incisions which I close, and I place the incisions in discrete locations to minimize the appearance. Usually, after a few days, the incisions close on their own.