Liposuction is a closed procedure, as such it does not require drainage.
When done with small cannulas, there are no large continuous cavities where lakes of fluid, or seromas, can accumulate. I don't know any surgeon that drains liposution with drains.
As far as leaving the incisions open, practices vary. I personally put two staples on each incision just to help it heal faster, but it still drains thru a little bit. I inject a lot of tumescent fluid, but frankly, I like to leave that fluid in as a reservoir of fluid for the patient to reabsorb over the next few days.
The best way to deal with the swelling is compression garments in combination with compression pads (Topifoam). This has the advantage of drastically reducing bruising.
When compression garments and pads are not used, it is not uncommon for the tissues to appear swollen for a while. At 12 days, It is too early to make a judgement. Do make your concerns known to your surgeon.
Check out the link below for a more in depth discussion of swelling post op.