Is it normal that every time I lift or flex my pectoral muscle my breast implants move?

Yes, it is normal for your implants to move when you flex your pectoral muscles.  This is called animation deformity.  It is not normal for you to have pain, but it may just be due to the fact that you are only 4 months postop.  If your pain isn't resolved in the next 1-2 months, talk to your surgeon to make sure everything is ok.  Best of luck!

If your goal is to become the strongest you can become, there is NO doubt that there will be a decrement in strength with submuscular augmentation.  If you have enough tissue above the muscle to camouflage the implant, then go above the muscle.  If you have very little tissue or diet down at certain times, you should consider submuscular implants with the understanding that there will be a small decrease in strength and that there may be a small chance to laterally displace the implants.  I have put submuscular implants in women who have bench pressed almost 300 lbs without ill effect, but it is always better for the patient to be fully informed. 

We see this with submuscular placement of implants.  It is not really a complication as much as a known sequelae of the procedure.  You can have your implants moved to in front of the muscle if you have enough tissue to cover them.  Just talk to your surgeon about your options.
Good luck,
Dr. T