Is there anything I can do to prevent my future implants from falling to the sides of my ribcage?

You need helpful input from your PS, but choosing the right diameter implant is important, as is limiting the lateral dissection.  Textured implants will 'stick' to the breast tissue / ribcage, and will be less likely to move.  Another option may be to use smooth implants over the muscle (smooth implants because they are less 'feel-able', over the muscle because the muscle has a tendency to force the implants outwards).

The reasons for lateral displacement of breast implants are: 1) Anatomy.  Medial dissection is limited to the lateral edge of the breast bone.  Cleavage is determined by how close the breasts are prior to surgery.  Pectus carinatum (high breast bone, narrow sloping chest) contribute to widely separated breasts. 2) Technique.  It is important not to dissect too laterally.  3)Type of implant.  Saline implants that are more fluid can "autodoissect" (make the pocket larger) by wave action.  Gel implants are solid and tend not to enlarge the pockets over time.  Textured implants allow ingrowth of tissue making the implant location more predictable and stable over time.  I concur that textured implants are a good choice in your case.

This question involves a detailed answer and in person assessment. Schedule a consultation with a board certified plastic surgeon to discuss your concerns. All the Best.