With FSMA the classification of food packaging varies based on the program. For the purposes of registering your facility and requiring a Preventative Control Qualified Individual, the FDA does NOT classify packaging as a "food ingredient" at this time. For the purposes of the Foreign Supplier Verification Program, the FDA DOES classify packaging (and any raw materials used to produce the packaging) as a "food ingredient". The FSVP states that the owner of the packaging materials at the time the materials arrive at the ports is responsible for having an FSVP program in place. The verbiage is as stated: "An importer is the U.S. owner or consignee of a food offered for import into the United States. If there is no U.S. owner or consignee, the importer is the U.S. agency or representative of the foreign owner of consignee at the time of entry, as confirmed in a signed statement of consent."
If you do not own the materials at the time of entry in the US, then ultimately you don't have to have an FSVP program. However as mentioned by Kellio, it would be in your best interest to have the necessary inspection, testing, and regulatory documentation in place.
I have started training my suppliers on the FSVP program. If anything, I want them to be prepared in the event they are audited. I am also putting together the plan as if it does apply to us, just in case our suppliers are audited and we can support them, thus avoiding any possible delays. I would also recommend including your foreign suppliers in your risk assessment and any mitigating steps.