As an update, the charge for the 2 tickets posted to my Citi account with the merchant simply listed as "Spirit Incentives", with no extra information (such as flight routing information) listed.

I'm comparing this to when you purchase directly from an airline, travel agent, or online travel agent, where the charge usually identifies the airline, dates travelling, fare class, and flight routing information.

Based on there being none of this information on my statement, I will assume that I will not be earning flight points for this ticket. (I know there is inconclusive and conflicting information in this thread as to whether one earns flight points on the first ticket.)