Facelift Disproportionately Fat Face?

Fullness in your lower cheeks is a very common trait that is quite difficult to correct completely, however improvement can be made surgically. Without seeing your photos, I'll answer the question in general terms. You are very young to have a facelift, but assuming this is what you're interested in exploring I'm going to address to the question of what surgical option is most likely to be effective.
There are few surgeon's that resect Bichat's fat pad during a facelift since it is in a territory referred to as tiger country because of the high conentration of facial nerve branches. You should find the ABPS BOARD CERTIFIED PLASTIC SURGEON in your area that is comfortable with this and has photos to share his experience with you.
Yes, once the fat pad is decompressed/reduced there will be sagging cheek tissues. These will need to be lifted and resuspended thus requiring a facelift.
Some resect this tissue with a tiny suction cannula but I think that's not a safe way of doing it since there are so many facial nerves there that control the movement in the corner of your mouth, suctioning is a blind technique and not my favorite way of doing it for that reason.
Lastly, I would warn you against your initial hunch of just tugging the skin laterally showing a significant improvement. There's plenty of people out there that would do that for a small fee. The tension will be there with a facelift but it will not fully correct the problem in the long term.
Eventually, the tissues from the pull will relax, the facelift scar will widen (over the years), and the cheek will bulge back through an unnatural "lateral sweep," where the wrinkles on your cheek sweep in the shape of a nike swoosh! It is potentially a pretty unnatual look. If you only lift up on your jawline and don't lift up your cheek, how will it look later on when your cheek continues to descend and your jawline didn't? My intent isn't to pose more problems, it is simply to reinforce the fact that your anatomy requires the skill of an ABPS Board Certified Plastic Surgeon that does Aesthetic Surgery.
The marionette lines can be improved with fillers, not a biggie. The turned down corners of your mouth is a little trickier but I've seen great great results just by using fillers causing some really nice optical illusions that show drastic improvements.

You sound too young for a facelift. Perhaps liposuction of your cheeks and jowls are sufficient at this time, however, I would not rule out the lipo combined with the facelift entirely.

The majority of patients seeking Facelift are age 50 and older.  A person in their 30's is generally not a candidate for a variety of reasons, but most importantly because the aging changes that can be addressed by Facelift are not present.  Secondly, Facelift is not usually considered a "facial slimming" procedure.  What would be most valuable to you would be a consultation with a Board Certified facial Plastic Surgeon or Plastic surgeon in your area.  There are some noninvasive treatment modalities, like Botox, which can reduce the size of your parotid gland and masseter muscles on a temporary basis.