If you read the GHB reference (33.5.1.1) from lajackson, you should find your answer there. For your question, the SS Secretary is in charge of recording second-hour SS attendance on 1st and 3rd Sundays.
Another possible way of reading this section from the handbook, is that the second-hour attendance should include all members who are participating in a second-hour class that day. And I'd ask the Bishop to give his direction as to how to interpret that, and how much effort to put into trying to determine attendance. For example, we have a Stake Presidency member in our unit who is quite often absent, and we always assume he is attending second-hour class in another part of the Stake -- but we don't verify if he was actually in a class or was meeting with somebody for an interview during 2nd hour. Or does an adult in the foyer count as long as they have a crying child with them?

And your Bishop can decide if he wants to simply assume that Primary Teachers can always be marked as attending SS/RS/EQ, or if he prefers that somebody verifies if they're in church each individual Sunday.