If you have amplified the dna with your primers then whatever their sequence they will be incorporated into the pcr product and will be fine for your sequencing so long as you supply the primers. Then you can check the sequence with BLAST and see where your primers are located. Primer sequences are too often badly reported in published papers, Primer blast using your primer sequences may give you an insight as to what is happening

The 2 primer sequences are the same except that the company sequence has an extra TAC at the 5prime end of the primer so the 2 primers will produce amplimers 3 bases different in length which you will not see on an agarose gel but the 3prime ends of the pri,ers are the same so noth should sequence well at the recommended 50c annealing for sequencing reactions